Shrinkage Estimation For The Diagonal Multivariate Natural Exponential Families
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Shrinkage Estimation For The Diagonal Multivariate Natural Exponential Families
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Author : Nikolas Siapoutis
language : en
Publisher:
Release Date : 2022
Shrinkage Estimation For The Diagonal Multivariate Natural Exponential Families written by Nikolas Siapoutis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
In this dissertation, we derive and study shrinkage estimators of the parameters of a high-dimensional diagonal natural exponential family of probability distributions. More broadly, we study shrinkage estimation of the parameters of distributions for which the diagonal entries of the covariance matrix are certain quadratic functions of the mean parameter. We propose two classes of semi-parametric shrinkage estimators for the mean of the population, and we construct unbiased estimators of the corresponding risk. We establish the asymptotic consistency and convergence rates for these shrinkage estimators under squared error loss as both $n$, the sample size, and $p$, the dimension, tend to infinity. Further, we specialize these results for the diagonal multivariate natural exponential families, which have been classified as consisting of the normal, Poisson, gamma, multinomial, negative multinomial, and hybrid classes of distributions, and we deduce consistency of our estimators. We deduce consistency of our estimators in the normal, gamma, and negative multinomial cases if $p n^{-1/3}(\log n)^{4/3} \rightarrow 0$ as $n,p \rightarrow \infty$, and for the Poisson and multinomial cases if $pn^{-1/2} \rightarrow 0$ as $n,p \rightarrow \infty$ To evaluate the performance of our mean shrinkage estimators, we carry out a simulation study for the multivariate gamma and multivariate Poisson classes of distributions. We begin by deriving the probability density functions of these two classes of distributions and establish some related regression properties. We propose several acceptance-rejection sampling algorithms and apply two versions of Metropolis algorithm to generate data from the multivariate gamma distribution, all-at-once and variable-at-a-time Metropolis algorithms. We propose reduction schemes for simulating observations from a multivariate Poisson distribution. We also approximate the probability density function of the multivariate Poisson distribution by applying the saddlepoint approximation method. Finally, we apply a variable-at-a-time Metropolis algorithm to generate data from the approximated probability density function. The simulation studies show the proposed estimators to achieve lower risk than the maximum likelihood estimator, thereby demonstrating the superiority of the proposed shrinkage estimators over the maximum likelihood estimator.
Multivariate Exponential Families A Concise Guide To Statistical Inference
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Author : Stefan Bedbur
language : en
Publisher: Springer
Release Date : 2021-10-08
Multivariate Exponential Families A Concise Guide To Statistical Inference written by Stefan Bedbur and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-08 with Mathematics categories.
This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.
Multivariate Natural Exponential Families
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Author : I-li Lu
language : en
Publisher:
Release Date : 1991
Multivariate Natural Exponential Families written by I-li Lu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Exponential families (Statistics) categories.
Multivariate Exponential Families
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Author : Jine-Phone Chou
language : en
Publisher:
Release Date : 1984
Multivariate Exponential Families written by Jine-Phone Chou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Estimation theory categories.
Bulletin Institute Of Mathematical Statistics
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Author : Institute of Mathematical Statistics
language : en
Publisher:
Release Date : 1994
Bulletin Institute Of Mathematical Statistics written by Institute of Mathematical Statistics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematical statistics categories.
Current Index To Statistics Applications Methods And Theory
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Author :
language : en
Publisher:
Release Date : 1996
Current Index To Statistics Applications Methods And Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematical statistics categories.
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Data Depth
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Author : Regina Y. Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Data Depth written by Regina Y. Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research. Information for our distributors: Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).
Simulating Data With Sas
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Author : Rick Wicklin
language : en
Publisher: SAS Institute
Release Date : 2013
Simulating Data With Sas written by Rick Wicklin and has been published by SAS Institute this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
Data simulation is a fundamental technique in statistical programming and research. Rick Wicklin's Simulating Data with SAS brings together the most useful algorithms and the best programming techniques for efficient data simulation in an accessible how-to book for practicing statisticians and statistical programmers. This book discusses in detail how to simulate data from common univariate and multivariate distributions, and how to use simulation to evaluate statistical techniques. It also covers simulating correlated data, data for regression models, spatial data, and data with given moments. It provides tips and techniques for beginning programmers, and offers libraries of functions for advanced practitioners. As the first book devoted to simulating data across a range of statistical applications, Simulating Data with SAS is an essential tool for programmers, analysts, researchers, and students who use SAS software. This book is part of the SAS Press program.
High Dimensional Probability
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Author : Roman Vershynin
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27
High Dimensional Probability written by Roman Vershynin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Business & Economics categories.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Theory Of Point Estimation
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Author : Erich L. Lehmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02
Theory Of Point Estimation written by Erich L. Lehmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Mathematics categories.
This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated, while an entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. This is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".