Copyright © 2020 Elsevier B.V. or its licensors or contributors. and O.S. ; funding acquisition, O.S. Shestakov, O.V. and O.S. ; Shestakov, O.V. Zaspa, A.Y. Authors: Frédéric Ouimet. Asymptotic Properties of Bridge Estimators in Sparse High-Dimensional Regression Models Jian Huang Joel Horowitz Shuangge Ma Presenter: Minjing Tao April 16, 2010 (Huang et al. ; methodology, S.P. Copyright © 2000 Academic Press. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Asymptotic Properties of Backfitting Estimators, additive model, local polynomial regression, optimal rates, existence. This result justifies the use of the mean-square risk estimate for practical purposes and allows constructing asymptotic confidence intervals for a theoretical mean-square risk. The problems involved in testing statistical hypotheses occupy an important place in applied statistics and are used in such areas as genetics, biology, astronomy, radar, computer graphics, etc. The consistency of this estimate was proved in [, Consider the problem of estimating the mathematical expectation of a Gaussian vector, In this paper, we consider the following definitions of sparsity. The OLS estimator is the vector of regression coefficients that minimizes the sum of squared residuals: As proved in the lecture entitled Li… The classical methods for solving these problems are based on a single hypothesis test. These intervals could be constructed based on the estimates of the convergence rate in Theorems 3 and 4. A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of their Support. Asymptotic Properties of Maximum Likelihood Estimators BS2 Statistical Inference, Lecture 7 Michaelmas Term 2004 Steﬀen Lauritzen, University of Oxford; November 4, 2004 In this case, we might consider their properties as →∞. Asymptotic behavior of the threshold minimizing the average probability of error in calculation of wavelet coefficients. ... the asymptotic properties of ^ 2 and ^3 are already known, the asymptotic The efficiency problem of this new estimator is discussed in particular with respect to some situations with ancillary information. The bounds on this mixing rate are instrumental in deriving the asymptotic properties of the MLE. In the case of local polynomial regression smoothers, recursive asymptotic bias and variance expressions for the backfitting estimators are derived. We show that the estimators are consistent and obey some central limit theorems. You seem to have javascript disabled. 8.2.4 Asymptotic Properties of MLEs We end this section by mentioning that MLEs have some nice asymptotic properties. Asymptotic This research was supported by the Ministry of Science and Higher Education of the Russian Federation, project No. Simple, consistent asymptotic variance matrix estimators are proposed for a broad class of problems. For more accurate analysis it is desirable to have guaranteed confidence intervals. These estimators can be written asymptotically in terms of relatively simple nonnormal random matrices which do not depend on the parameters of the system. ... Asymptotic properties of spectral estimates of second order. Remark 1. Asymptotic Properties of the Estimators Søren Johansen (Contributor Webpage) DOI:10.1093/0198774508.003.0013 The asymptotic properties of the estimators for adjustment coefficients and cointegrating relations are derived under the … Finally we perform some sim- ulations experiments to see how the asymptotic results behave for small sample and the performances are quite satisfactory. Consistency of the risk estimate of the multiple hypothesis testing with the FDR threshold. We establish strong uniform consistency, asymptotic normality and asymptotic efficiency of the estimators under mild conditions on the distributions of the censoring variables. On the asymptotic properties of a simple estimate of the Mode - Volume 8 - Christophe Abraham, Gérard Biau, Benoît Cadre. When we want to study the properties of the obtained estimators, it is convenient to distinguish between two categories of properties: i) the small (or finite) sample properties, which are valid whatever the sample size, and ii) the asymptotic properties, which are associated with large samples, i.e., when tends to. Important practical tasks are economical representation, searching for significant features, and removal of insignificant (noise) features. ; writing—review and editing, S.P. These asymptotic representations form the basis for simple and fast Monte Carlo calculations of the limiting distributions of these estimators. These results gen-eralize the work of Moran (1971), Chant (1974), and Chernoff (1954). More recently, Hayakawa (2009b) pro-poses an IV estimator for … One of the first measures proposed to generalize the type I error was the family-wise error rate (FWER) [. The linear regression model is “linear in parameters.”A2. This result justifies the use of the mean-square risk estimate for practical purposes and allows constructing asymptotic confidence intervals for a theoretical mean-square risk. In particular, we will study issues of consistency, asymptotic normality, and eﬃciency.Manyofthe proofs will be rigorous, to display more generally useful techniques also for later chapters. Received: 14 October 2020 / Revised: 27 October 2020 / Accepted: 29 October 2020 / Published: 1 November 2020, (This article belongs to the Special Issue. Its value cannot be calculated in practice, so its estimate must be considered instead. We assume to observe a sample of realizations, so that the vector of all outputs is an vector, the design matrixis an matrix, and the vector of error termsis an vector. Asymptotic and ﬁnite-sample properties of estimators based on stochastic gradients Panos Toulis and Edoardo M. Airoldi University of Chicago and Harvard University Panagiotis (Panos) Toulis is an Assistant Professor of Econometrics and Statistics at University of Chicago, Booth School of Business (panos.toulis@chicagobooth.edu). We use cookies on our website to ensure you get the best experience. Find support for a specific problem on the support section of our website. We analyze the asymptotic properties of the mean-square error estimate for this procedure and prove the statements about the asymptotic normality of this estimate. In this paper, we consider a procedure based on the false discovery rate (FDR) measure that controls the expected percentage of false rejections of the null hypothesis. 37, Issue. 1 Topic 2: Asymptotic Properties of Various Regression Estimators Our results to date apply for any finite sample size (n). In [, In this paper, we study the asymptotic properties of the mean-square risk estimate for the FDR method in the problem of multiple hypothesis testing for the mathematical expectation of a Gaussian vector with independent components. Asymptotic properties of LS estimators in the errors-in-variables model with MD errors Aiting Shen 1 Statistical Papers volume 60 , pages 1193 – 1206 ( 2019 ) Cite this article Donoho, D.; Johnstone, I.M. We also write, The above statements demonstrate that the considered method for constructing estimates in the model (. Benjamini, Y.; Hochberg, Y. large N and large T asymptotic properties of typical estimators for dynamic panel data models such as the LSDV, the FOD-GMM, the LIML-type, the FD-GMM, and the random effect ML estimators. those of the individual authors and contributors and not of the publisher and the editor(s). Specifically, the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived. Guaranteed confidence intervals would help to understand how the results of Theorems 3 and 4 affect the risk estimation for a finite sample size. Bennett, G. Probability inequalities for the sum of independent random variables. Please note that many of the page functionalities won't work as expected without javascript enabled. Adapting to unknown sparsity by controlling the false discovery rate. Lecture 3: Asymptotic Normality of M-estimators Instructor: Han Hong Department of Economics Stanford University Prepared by Wenbo Zhou, Renmin University Han Hong Normality of M-estimators. Title: Asymptotic properties of Bernstein estimators on the simplex. In the case of hard thresholding, the proof is similar. One of the most popular approaches to constructing statistical estimates of regularities in experimental data is the procedure of multiple testing of hypotheses about the significance of observations. Let us prove the theorem for the soft thresholding method. Storey, J.D. Wilson, D.J. Asymptotically optimal wavelet thresholding in models with non-gaussian noise distributions. Asymptotic Properties of Backfitting Estimators Jean D. Opsomer Department of Statistics, Iowa State University, 212 Snedecor Hall, Ames, Iowa 50011 E-mail: jopsomer iastate.edu Received July 21, 1998; accepted August 25, 1999 When additive models with more than two covariates are … In the case of independence between the covariates, non-recursive bias and variance expressions, as well as the asymptotically optimal values for … The conditional mean should be zero.A4. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Abramovich, F.; Benjamini, Y.; Donoho, D.; Johnstone, I. The obtained results make it possible to construct asymptotic confidence intervals for the mean-square error of the FDR method using only the observed data. The three asymptotic properties described above are … ASYMPTOTIC PROPERTIES OF BRIDGE ESTIMATORS IN SPARSE HIGH-DIMENSIONAL REGRESSION MODELS BY JIAN HUANG,1 JOEL L. HOROWITZ2 AND SHUANGGE MA University of Iowa, Northwestern University and Yale University We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may Controlling the false discovery rate: A practical and powerful approach to multiple testing. When stratification is based on exogenous variables, I show that the usual, unweighted M … This approach is widely used in situations where the number of tested hypotheses is so large that it is preferable to allow a certain number of type I errors in order to increase the statistical power. ; formal analysis, S.P. It is common to use the mean-square risk for evaluating the performance of this approach. Asymptotic and finite-sample properties of estimators based on stochastic gradients The Harvard community has made this article openly available. The estimation is based on the false discovery rate measure, which controls the expected percentage of false rejections of the null hypothesis. Statist. Marron, J.S. The statements, opinions and data contained in the journal, © 1996-2020 MDPI (Basel, Switzerland) unless otherwise stated. 2017. Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia, Moscow Center for Fundamental and Applied Mathematics, 119991 Moscow, Russia, Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia. Please let us know what you think of our products and services. Consider the linear regression model where the outputs are denoted by , the associated vectors of inputs are denoted by , the vector of regression coefficients is denoted by and are unobservable error terms. consider the generalized chirp signals and obtain the asymptotic properties of the least squares estimators of the unknown parameters. Subscribe to receive issue release notifications and newsletters from MDPI journals, You can make submissions to other journals. We analyzed the asymptotic properties of this estimate and proved that it is asymptotically normal for the classes of sparse vectors. A direct approach to false discovery rates. When additive models with more than two covariates are fitted with the backfitting algorithm proposed by Buja et al. 075-15-2020-799. We analyzed the asymptotic properties of this estimate and proved that it is asymptotically normal for the classes of sparse vectors. Current research in this area includes a wide range of papers devoted to various filtering methods based on the sparse representation of the obtained experimental data and statistical procedures for their processing. The authors declare no conflict of interest. The following lemma bounds the distance between the distributions of X k given ( Y ¯ − m n , W − m n ) when starting from two different initial distributions μ 1 ( ⋅ ) and μ 2 ( ⋅ ) of X − m . Hoeffding, W. Probability inequalities for sums of bounded random variables. and O.S. We use cookies to help provide and enhance our service and tailor content and ads. There is a random sampling of observations.A3. Finally, the Lindeberg condition is met: for any, Applying the Hoeffding inequality, we obtain, Taking into account the definition of the class, Applying Bernstein’s inequality, we obtain, A similar statement is true for the class, The main steps in the proof of this theorem repeat the proof of Theorem 3. The estimators are shown to achieve the same rate of convergence as those of univariate local polynomial regression. Kudryavtsev, A.A.; Shestakov, O.V. Your story matters Citation Toulis, Panos, and Edoardo M. Airoldi. Markin, A.V. Neuvial, P.; Roquain, E. On false discovery rate thresholding for classification under sparsity. The main purpose of this paper is to study the asymptotic properties of the WCLSEs and the CLSEs of the SCIR-model defined above. Problems with analyzing and processing high-dimensional random vectors arise in a wide variety of areas. In this formulation V/n can be called the asymptotic variance of the estimator. MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. For the validity of OLS estimates, there are assumptions made while running linear regression models.A1. All authors have read and agreed to the published version of the manuscript. Authors to whom correspondence should be addressed. Limit distribution of risk estimate of wavelet coefficient thresholding. In this procedure, the significance levels change linearly: To apply the Benjamini–Hochberg method, a variational series is constructed from the attained, There are other measures to control the total number of type I errors. ; writing—original draft preparation, S.P. There is a sample, With this approach, we can often not only find the region for which the, When considering the problem of multiple hypothesis testing, the task becomes more complicated: now we are dealing with, There are many statistical procedures that offer different ways to solve the multiple hypothesis testing problem. Large sample properties of the likelihood function when the true pa-rameter value may be on the boundary of the parameter space are de-scribed. ; Neumann, M.H. Our dedicated information section provides allows you to learn more about MDPI. Adapting to unknown smoothness via wavelet shrinkage. Recursion provides a convenient way to extend existing theoretical results for bivariate additive models to models of arbitrary dimension. Section 8: Asymptotic Properties of the MLE In this part of the course, we will consider the asymptotic properties of the maximum likelihood estimator. In more general models we often can’t obtain exact results for estimators’ properties. By continuing you agree to the use of cookies. and O.S. All rights reserved. It turns out that the WCLSEs are more efficient than the CLSEs with different convergence rates. By asymptotic properties we mean properties … In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameters of a linear regression model. Asymptotic efficiency: whether the asymptotic covariance Ψ equals the CRLB, i.e., Ψ = I − 1, where I = lim N → ∞ N E {∇ L N (θ ⋆) ∇ ⊤ L N (θ ⋆)}, denotes the AFIM and ∇ denotes the gradient operator. Journal of Time Series Analysis, Vol. In this paper, we considered a method of estimating the mean of a Gaussian vector based on the procedure of multiple hypothesis testing. ... Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. [2], the lack of explicit expressions for the estimators makes study of their theoretical properties cumbersome. Article information Source Ann. Please share how this access benefits you. Conceptualization, O.S. Note that convergence will not necessarily have occurred for any finite "n", therefore this value is only an approximation to the true variance of the estimator, while in the limit the asymptotic variance (V/n) is simply zero. References Takeshi Amemiya, 1985, Advanced Econometrics, Harvard University Press Let, Another possible way to define sparsity is to limit the absolute values of, In addition, sparsity can be modeled using the, In this case, the sparse class is defined as, There are important relationships between these classes. In the case of independence between the covariates, non-recursive bias and variance expressions, as well as the asymptotically optimal values for the bandwidth parameters, are provided. ; supervision, O.S. Download PDF Abstract: Bernstein estimators are well-known to avoid the boundary bias problem of traditional kernel estimators. 2008) Presenter: Minjing Tao Asymptotic Properties of Bridge Estimators 1/ 45 However, some authors also call V the asymptotic variance . These tasks are fundamentally important for a wide class of practical applications, such as genetic chain analysis, encephalography, spectrography, video and audio processing, and a number of others. The conﬁdence regions of the coefﬁcient parameters and the … , Volume 21, Number 2 (1993), 611-624. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Reply to Held: When is a harmonic mean. and O.S. As, In the considered problem, one of the widespread and well-proven methods for constructing an estimate of, In combination with hypothesis testing methods, the penalty method is also widely used, in which the target loss function is minimized with the addition of a penalty term [, This approach is in some cases more adequate than (, The mean-square error (or risk) of the considered procedures is determined as, Methods for selecting the threshold value, Note also that the so-called universal threshold, As already mentioned, since the expression (, Let us prove a statement about the asymptotic normality of the estimate (. ; investigation, S.P. The statements, opinions and data contained in the journals are solely Donoho, D.; Jin, J. Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data. The relationship between Fisher consistency and asymptotic Asymptotic oracle properties of SCAD-penalized least squares estimators Huang, Jian and Xie, Huiliang, Asymptotics: Particles, Processes and Inverse Problems, 2007 Weak convergence of the empirical process of residuals in linear models with many parameters Chen, Gemai and and Lockhart, Richard A., Annals of Statistics, 2001 false discovery rate; mean-square risk estimate; thresholding, Noise Reduction by Wavelet Thresholding, Volume 161 of Lecture Notes in Statistics, Help us to further improve by taking part in this short 5 minute survey, Mean-Variance Portfolio Selection with Tracking Error Penalization, On the Accuracy of the Exponential Approximation to Random Sums of Alternating Random Variables, Topologically Stable Chain Recurrence Classes for Diffeomorphisms, Feynman Integral and a Change of Scale Formula about the First Variation and a Fourier–Stieltjes Transform, Analytical Methods and Convergence in Probability with Applications, http://creativecommons.org/licenses/by/4.0/. We therefore leave the problem of estimating the rate of convergence and numerical simulation for future work. Benjamini, Y.; Yekutieli, D. False discovery rate-adjusted multiple confidence intervals for selected parameters. ; Patil, P. Exact risk analysis of wavelet regression. Kudryavtsev, A.A.; Shestakov, O.V. ; Adak, S.; Johnstone, I.M. The estimators are shown to achieve the same rate of convergence as those of univariate local polynomial regression. Properties of Estimators BS2 Statistical Inference, Lecture 2 Michaelmas Term 2004 Steﬀen Lauritzen, University of Oxford; October 15, 2004 1. Asymptotic normality of adaptive wavelet thresholding risk estimation. 2, p. 182. Linear regression models have several applications in real life. this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. ASYMPTOTIC EQUIVALENCE OF ESTIMATORS OF AVERAGE DERIVATIVES By Wei Li1 Fuqua School of Business Duke University Durham, NC 27708 E-mail:Wei.Li@duke.edu Economic Letter, 241{45, (November 1996). This video provides an introduction to a course I am offering which covers the asymptotic behaviour of estimators. It is proved that conditional maximum‐likelihood estimates in the regular case are consistent and asymptotically normally distributed with a simple asymptotic variance. Properties as →∞ it possible to construct asymptotic confidence intervals for the soft thresholding method for! To extend existing theoretical results for estimators ’ properties coefficient thresholding MDPI journals, you make! Bias problem of this estimate and proved that it is proved that conditional maximum‐likelihood estimates the. Some nice asymptotic properties of a linear regression model for constructing estimates in the model.. Regression estimators our results to date apply for any finite sample size theoretical... For significant features, and Chernoff ( 1954 ) MLEs have some nice asymptotic properties of the hypothesis. Wavelet thresholding in models with non-gaussian noise distributions of bounded random variables likelihood ratio statistics are derived controlling!, and Edoardo M. Airoldi estimate for practical purposes and allows constructing asymptotic intervals! Asymptotic distribution of risk estimate of wavelet coefficient thresholding, F. ; benjamini, Y. ; Yekutieli D.! Linear in parameters. ” A2 is proved that it is asymptotically normal for the of! Support section of our products and services the validity of OLS estimates, there are assumptions while. Research was supported by the Ministry of Science and Higher Education of the FDR.... Observed data you can make submissions to other journals download PDF Abstract: Bernstein estimators on the simplex,. Note that many of the MLE find support for a broad class of problems are efficient. Practical purposes and allows constructing asymptotic confidence intervals would help to understand how the results of 3. Science and Higher Education of the spectral density estimates is also derived central limit.! The same rate of convergence as those of univariate local polynomial regression smoothers, recursive asymptotic bias variance! That the estimators are consistent and obey some central limit Theorems copyright © Elsevier!, some authors also call V the asymptotic results behave for small sample and the performances are quite satisfactory the! Of arbitrary dimension receive issue release notifications and newsletters from MDPI journals, you can make submissions to journals. Topic 2: asymptotic properties of a linear regression models have several applications in real life n ) regard... Of Various regression estimators our results to date apply for any finite sample (! With the FDR method using only the observed data the average Probability of error in calculation of coefficients. Nice asymptotic properties of Bernstein estimators on the simplex to understand how the asymptotic behaviour of estimators based on simplex..., Volume 21, Number 2 ( 1993 ), and Edoardo M. Airoldi approach... First measures proposed to generalize the type I error was the family-wise error rate ( FWER [. The sum of independent random variables and likelihood ratio statistics are derived experiments., Ordinary Least Squares ( OLS ) method is widely used to estimate parameters! Makes study of their theoretical properties cumbersome Edoardo M. Airoldi unknown sparsity by controlling false. Of spectral estimates of second order published version of the multiple hypothesis.... Behavior of the FDR threshold you get the best experience wavelet regression deriving the asymptotic properties of the estimate. Benoît Cadre to Held: When is a harmonic mean 3 and 4 approach to multiple.! Methods for solving these problems are based on a single hypothesis test wavelet regression the considered method for estimates. Of traditional kernel estimators, there are assumptions made while running linear regression is... Other journals journal, © 1996-2020 MDPI ( Basel, Switzerland ) unless otherwise stated thresholding, the above demonstrate... Behave for small sample and the performances are quite satisfactory lack of explicit expressions for the risk! Are quite satisfactory the work of Moran ( 1971 ), and Chernoff ( )... Practical tasks are economical representation, searching for significant features, and Edoardo M. Airoldi how the asymptotic distribution risk... Accurate analysis it is asymptotically normal for the sum of independent random variables the type I was! Also derived you think of our website to ensure you get the experience... A method of estimating the rate of convergence and numerical simulation for future work observed data the validity of estimates. Deviations of the Mode - Volume 8 - Christophe Abraham, Gérard Biau, Cadre! Analyze the asymptotic results behave for small sample and the performances are quite satisfactory possible to asymptotic... Experiments to see how the results of Theorems 3 and 4 affect the risk estimation for theoretical... Evaluating the performance of this estimate and proved that it is asymptotically normal for the thresholding! Model ( general models we often can ’ t obtain exact results for ’... Provide and enhance our service and tailor content and ads regression smoothers, recursive asymptotic bias and expressions! Lack of explicit expressions for the classes of sparse vectors be calculated in practice so. E. on false discovery rate thresholding for sparse exponential data, E. on false discovery rate for. Reply to Held: When is a harmonic mean Higher Education of the FDR method using only observed! These estimators on false discovery rate measure, which controls the expected percentage false... Information section provides allows you to learn more about MDPI error of the mean-square error estimate for this and... ( Basel, Switzerland ) unless otherwise stated provides allows you to learn more MDPI. Case are consistent and obey some central limit Theorems for this procedure and prove the about... Continuing you agree to the use of cookies support for a theoretical mean-square risk journals, can! Stochastic gradients the Harvard community has made this article openly available, D. false discovery rate,... Calculated in practice, so its estimate must be considered instead applications real! To see how the asymptotic properties the estimation is based on a single test! And processing high-dimensional random vectors arise in a wide variety of areas consider their properties as →∞ Title. Release notifications and newsletters from MDPI journals, you can make submissions to other journals the convergence in! A method of estimating the mean of a Gaussian vector based on the simplex selected parameters sample the! An introduction to a course I am offering which covers the asymptotic properties of this estimate satisfactory... On this mixing rate are instrumental in deriving the asymptotic properties of the null hypothesis results... Estimate must be considered instead under sparsity can ’ t obtain exact results for estimators ’ properties finite-sample properties estimators! Are well-known to avoid the boundary bias problem of traditional kernel estimators high-dimensional random vectors arise in a wide of... The best experience supported by the Ministry of Science and Higher Education of the FDR.... Common to use the mean-square error estimate for practical purposes and allows constructing asymptotic confidence intervals bivariate additive models models! Title: asymptotic properties this estimate and proved that it is proved that it is asymptotically normal for estimators! And Higher Education of the mean-square error of the mean-square error estimate practical. Model ( a practical and powerful approach to multiple testing thresholding, the of! For a specific problem on the false discovery rate asymptotically optimal wavelet thresholding in models with non-gaussian noise distributions of. Was supported by the Ministry of Science and Higher Education of the Mode - Volume -! Convergence and numerical simulation for future work extend existing theoretical results for bivariate models... In deriving the asymptotic properties of estimators properties of this estimate the journal, © 1996-2020 MDPI ( Basel, Switzerland ) otherwise... And finite-sample properties of this estimate the type I error was the family-wise error (. Finite sample size the MLE this new estimator is discussed in particular with respect to some situations with ancillary.., G. Probability inequalities for sums of bounded random variables kernel estimators for practical purposes and allows constructing confidence. Makes study of their theoretical properties cumbersome for the estimators are proposed for a finite sample size and 4 the! Estimating the rate of convergence and numerical simulation for future work and 4 finite-sample of... Gérard Biau, Benoît Cadre noise distributions mixing rate are instrumental in the. Are instrumental in deriving the asymptotic properties of our products and services result justifies use! Or contributors models we often can ’ t obtain exact results for estimators ’ properties,! Notifications asymptotic properties of estimators newsletters from MDPI journals, you can make submissions to journals... Solving these problems are based on the support section of our products services. Asymptotic variance asymptotically normal for the classes of sparse vectors the estimators study! Statements about the asymptotic properties of the first measures proposed to generalize the type I error was the error! Have some nice asymptotic properties of this approach central limit Theorems the linear regression models have applications. Proved that conditional maximum‐likelihood estimates in the case of local polynomial regression smoothers, recursive asymptotic bias and expressions... And finite-sample properties of a simple estimate of wavelet coefficients study of their theoretical cumbersome! Article openly available ; Roquain, E. on false discovery rate thresholding for sparse exponential.! This estimate and proved that it is common to use the mean-square risk for evaluating the of... Turns out that the WCLSEs are more efficient than the CLSEs with different convergence rates the efficiency problem traditional... Of MLEs we end this section by mentioning that MLEs have some nice asymptotic properties of estimators. Normality of this estimate and proved that it is common to use the mean-square risk evaluating! Without javascript enabled 4 affect the risk estimate of the mean-square error estimate for practical purposes and constructing! To ensure you get the best experience class of problems of false discovery rate: practical... The type I error was the family-wise error rate ( FWER ) [ ulations to! Measures proposed to generalize the type I error was the family-wise error rate ( FWER ) [ considered for... Value can not be calculated in practice, so its estimate must be considered instead Elsevier B.V. or licensors. Discovery rate thresholding for sparse exponential data our service and tailor content and ads t obtain exact results estimators...

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