Van der Vaart A.W. Asymptotic Statistics

Cambridge University Press, 2000. — 462 p. — (Cambridge Series in Statistical and Probabilistic Mathematics). — ISBN: 0521784506, 9780521784504Here 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.Stochastic convergence
The delta-method
Moment estimators
M- and Z-estimators
Contiguity
Local asymptotic normality
Efficiency of estimators
Limits of experiments
Bayes procedures
Projections
U-statistics
Rank, sign, and permutation statistics
Relative efficiency of tests
Efficiency of tests
Likelihood ratio tests
Chi-square tests
Stochastic convergence in metric spaces
Empirical processes
The functional delta-method
Quantiles and order statistics
L-statistics
The bootstrap
Nonparametric density estimation
Semiparametric models.