Mathematical Statistics: Basic Ideas and Selected Topics, Volume II, Volume 2Mathematical Statistics: Basic Ideas and Selected Topics, Volume II presents important statistical concepts, methods, and tools not covered in the authors' previous volume. This second volume focuses on inference in non- and semiparametric models. It not only reexamines the procedures introduced in the first volume from a more sophisticated point o |
Contents
INTRODUCTION AND EXAMPLES | |
TOOLS FOR ASYMPTOTIC ANALYSIS | |
DISTRIBUTIONFREE UNBIASED AND EQUIVARIANT PROCEDURES | |
INFERENCE IN SEMIPARAMETRIC MODELS | |
MONTE CARLO METHODS | |
NONPARAMETRIC INFERENCE FOR FUNCTIONS OF ONE VARIABLE | |
PREDICTION AND MACHINE LEARNING | |
SOME AUXILIARY RESULTS | |
E SOLUTIONS FOR VOLUME II | |
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Common terms and phrases
approximation arg max arg min assume asymptotic Bayes risk Bayesian bias bootstrap bounded Brownian bridge C₁ classification compute consider continuous corresponding covariance cross validation D₁ defined denote dimensional Example exponential exponential family f₁ finite follows Gaussian given h₁ Hint independent inequality influence function invariant k₁ kernel Lemma Let X1 linear Markov chain matrix maximal maximum likelihood method minimax minimizer Monte Carlo multivariate n₁ nonparametric Note obtain optimal P₁ parameter parametric model probability Proof Proposition R₁ random variables regression regular rejective sampling result sample semiparametric models Show sieve statistic sufficient statistic Suppose T₁ U₁ UMVU estimate unbiased uniformly v₁ variance vector weak convergence X₁ Y₁ Z₁ θο μ₁ σ² σο