Asymptotics in Statistics

by ;
Edition: 2nd
Format: Hardcover
Pub. Date: 2000-06-01
Publisher(s): Springer Verlag
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Summary

This volume is the second edition of a work that presents a coherent introduction to the subject of asymptotic statistics as it has developed in the past 50 years. The second edition differs from the first in that it has been made more 'reader friendly'. It also includes a new chapter, Chapter 4, on Gaussian and Poisson experiments because of their growing role in the field, especially in nonparametrics and semi-parametrics. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been ampliefied. Much of the material has been taught in a second year graduate course at Berkeley for 30 years. It represents a link between traditional material including maximum likelihood, and Wald's Theory of Statistical Decision Functions together with comparison and distances for experiments. This volume is not intended to replace monographs on specialized subjects, but it will help to place them in a coherent perspective.Lucien Le Cam is Professor of Statistics and Mathematics (Emeritus) at the University of California, Berkeley. He is the author of numerous papers on asymptotics and Asymptotic Methods in Statistical Decision Theory, Springer Verlag (1986). He was co-editor, with J. Neyman and E. Scott of the Berkeley Symposia on Mathematical Statistics and Probability. Grace Lo Yang is Professor, Department of Mathematics, University of Maryland, College Park. She is a long time holder of a Faculty Appointment at the National Institute of Standards and Technology, Gaithersburg, MD. Her research activities include stochastic modeling in physical sciences and theory of incomplete data.

Author Biography

Grace Lo Yang is Professor, Department of Mathematics, at the University of Maryland, College Park.

Table of Contents

Dedicatory Note v
Preface to the Second Edition vii
Preface to the First Edition ix
Introduction
1(5)
Experiments, Deficiencies, Distances
6(28)
Comparing Risk Functions
6(7)
Deficiency and Distance between Experiments
13(5)
Likelihood Ratios and Blackwell's Representation
18(9)
Further Remarks on the Convergence of Distributions of Likelihood Ratios
27(4)
Historical Remarks
31(3)
Contiguity -- Hellinger Transforms
34(16)
Contiguity
34(8)
Hellinger Distances, Hellinger Transforms
42(6)
Historical Remarks
48(2)
Gaussian Shift and Poisson Experiments
50(27)
Introduction
50(1)
Gaussian Experiments
51(13)
Poisson Experiments
64(10)
Historical Remarks
74(3)
Limit Laws for Likelihood Ratios
77(40)
Introduction
77(1)
Auxiliary Results
77(17)
Lindeberg's Procedure
78(4)
Levy Splittings
82(1)
Paul Levy's Symmetrization Inequalities
83(1)
Conditions for Shift-Compactness
84(2)
A Central Limit Theorem for Infinitesimal Arrays
86(3)
The Special Case of Gaussian Limits
89(3)
Peano Differentiable Functions
92(2)
Limits for Binary Experiments
94(13)
Gaussian Limits
107(7)
Historical Remarks
114(3)
Local Asymptotic Normality
117(58)
Introduction
117(2)
Locally Asymptotically Quadratic Families
119(5)
A Method of Construction of Estimates
124(10)
Some Local Bayes Properties
134(6)
Invariance and Regularity
140(10)
The LAMN and LAN Conditions
150(12)
Additional Remarks on the LAN Conditions
162(2)
Wald's Tests and Confidence Ellipsoids
164(4)
Possible Extensions
168(2)
Historical Remarks
170(5)
Independent, Identically Distributed Observations
175(65)
Introduction
175(2)
The Standard i.i.d. Case: Differentiability in Quadratic Mean
177(9)
Some Examples
186(8)
Some Nonparametric Considerations
194(20)
Bounds on the Risk of Estimates
214(15)
Some Cases Where the Number of Observations Is Random
229(6)
Historical Remarks
235(5)
On Bayes Procedures
240(23)
Introduction
240(1)
Bayes Procedures Behave Nicely
241(5)
The Bernstein--von Mises Phenomenon
246(2)
A Bernstein--von Mises Result for the i.i.d. Case
248(9)
Bayes Procedures Behave Miserably
257(4)
Historical Remarks
261(2)
Bibliography 263(15)
Author Index 278(3)
Subject Index 281

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