Asymptotic Statistics

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Cambridge University Press, Jun 19, 2000 - Mathematics - 443 pages
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Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. In addition to most of the standard topics of an asymptotics course--likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures--the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, one of the book's unifying themes that mainly entails the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation.
 

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Contents

Stochastic Convergence
5
Delta Method
25
Moment Estimators
35
Contiguity
85
Local Asymptotic Normality
92
Efficiency of Estimators
108
Limits of Experiments
125
Bayes Procedures
138
Likelihood Ratio Tests
227
ChiSquare Tests
242
Stochastic Convergence in Metric Spaces
255
Empirical Processes
265
Functional Delta Method
291
Quantiles and Order Statistics
304
LStatistics
316
Bootstrap
326

Projections
153
Statistics
161
Rank Sign and Permutation Statistics
173
Relative Efficiency of Tests
192
Efficiency of Tests
215
Nonparametric Density Estimation
341
Semiparametric Models
358
References
433
Index
439
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