This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including 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, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
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Efficiency of Estimators
Limits of Experiments
Likelihood Ratio Tests
Stochastic Convergence in Metric Spaces
Functional Delta Method
Quantiles and Order Statistics
Nonparametric Density Estimation
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alternative apply approximation argument assume asymptotically normal Banach space bounded Chapter closed consider consistent constant contained continuous converges converges in distribution corresponding defined definition density depends derivative difference differentiable display distribution function efficient empirical equal equation Example exists expectation experiment finite fixed follows function F given gives hence independent inequality influence function instance integral interval known lemma likelihood ratio limit limit distribution linear matrix maximal maximum likelihood estimator mean measurable method null hypothesis observations obtain parameter preceding probability problem projection proof prove quantile random range relative respectively satisfies score score function sequence Show side space square standard statistic subset sufficiently Suppose takes tangent term theorem true uniform uniformly values variables variance vector yields zero