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Maximum Penalized Likelihood Estima Volume 1

by

Maximum Penalized Likelihood Estima Volume 1 Cover

 

Synopses & Reviews

Publisher Comments:

This book is intended for graduate students in statistics and industrial mathematics, as well as researchers and practitioners in the field. We cover both theory and practice of nonparametric estimation. The text is novel in its use of maximum penalized likelihood estimation, and the theory of convex minimization problems (fully developed in the text) to obtain convergence rates. We also use (and develop from an elementary view point) discrete parameter submartingales and exponential inequalities. A substantial effort has been made to discuss computational details, and to include simulation studies and analyses of some classical data sets using fully automatic (data driven) procedures. Some theoretical topics that appear in textbook form for the first time are definitive treatments of I.J. Good's roughness penalization, monotone and unimodal density estimation, asymptotic optimality of generalized cross validation for spline smoothing and analogous methods for ill-posed least squares problems, and convergence proofs of EM algorithms for random sampling problems.

Synopsis:

This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.

Synopsis:

This text deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints such as unimodality and log-concavity. It is intended for graduate students in statistics, applied mathematics, and operations research, as well as for researchers and practitioners in the field. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into some of the generally applicable technical tools from probability theory (discrete parameter martingales) and applied mathematics (boundary, value problems and integration by parts tricks.) Convexity and convex optimization, as applied to maximum penalized likelihood estimation, receive special attention. The authors are with the Statistics Program of the Department of Food and Resource Economics in the College of Agriculture at the University of Delaware.

Description:

Includes bibliographical references (p. [489]-498) and index.

Table of Contents

Parametric Maximum Likelihood Estimation * Parametric Maximum Likelihood Estimation in Action * Kernel Density Estimation * Maximum Likelihood Density Estimation * Monotone and Unimodal Densities * Choosing the Smoothing Parameter * Nonparametric Density Estimation in Action * Convex Minimization in Finite Dimensional Spaces * Convex Minimization in Infinite Dimensional Spaces * Convexity in Action

Product Details

ISBN:
9780387952680
Author:
Eggermont, Paul
Author:
LaRiccia, Vincent
Author:
Eggermont, Paul
Author:
Eggermont, P.P.B.
Author:
Lariccia, V.
Author:
LaRiccia, V.N.
Author:
Eggermont, P. P. B.
Publisher:
Springer
Location:
New York
Subject:
General
Subject:
Statistics
Subject:
Estimation theory
Subject:
Probability & Statistics - General
Subject:
Density Estimation
Subject:
Maximum Likelihood
Subject:
Maximum Penalized Likelihood
Subject:
Regression analysis
Subject:
Statistical Theory and Methods
Subject:
Operations Research/Decision Theory
Subject:
Operations Research/Decision Theo
Subject:
ry This reference book is intended for graduate students and researchers in statistics, industrial and engineering mathematics, and operations research.
Subject:
Health and Medicine-General
Subject:
Operation Research/Decision Theory
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Springer Series in Statistics
Series Volume:
13574
Publication Date:
June 2001
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
528
Dimensions:
235 x 155 mm 2020 gr

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Related Subjects

Health and Self-Help » Health and Medicine » General
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Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Maximum Penalized Likelihood Estima Volume 1 New Hardcover
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$219.75 In Stock
Product details 528 pages Springer-Verlag Telos - English 9780387952680 Reviews:
"Synopsis" by , This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.
"Synopsis" by , This text deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints such as unimodality and log-concavity. It is intended for graduate students in statistics, applied mathematics, and operations research, as well as for researchers and practitioners in the field. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into some of the generally applicable technical tools from probability theory (discrete parameter martingales) and applied mathematics (boundary, value problems and integration by parts tricks.) Convexity and convex optimization, as applied to maximum penalized likelihood estimation, receive special attention. The authors are with the Statistics Program of the Department of Food and Resource Economics in the College of Agriculture at the University of Delaware.
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