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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Local Asymptotic Normality
Efficiency of Estimators
Limits of Experiments
Likelihood Ratio Tests
Stochastic Convergence in Metric Spaces
Functional Delta Method
Quantiles and Order Statistics
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approximation assume asymptotic variance asymptotically efficient asymptotically normal asymptotically optimal bootstrap bounded central limit theorem Chapter chi-square confidence interval consistent continuous converges in distribution converges in probability converges to zero covariance matrix defined delta method density derivative differentiable in quadratic distribution function empirical distribution empirical process equal equation estimator 9n estimator sequence Example exists exponential finite Fisher information fixed follows function F Gaussian given hence inequality kernel large numbers likelihood ratio statistic limit distribution limit experiment linear map 9 maximal maximum likelihood estimator mean zero measurable function norm normal distribution null hypothesis observations obtain orthogonal parameter 9 power function preceding display projection proof quadratic mean quantile random sample random variables random vectors rank statistics right side satisfies score function sequence of tests sequence Tn Show standard normal submodel subset Suppose tangent set term underlying distribution uniform uniformly values