(Wiley Series in Probability and Statistics) 1st Edition
by Marc S. Paolella (Author)
A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field
This
clear and accessible book for beginning graduate students offers a
practical and detailed approach to the field of statistical inference,
providing complete derivations of results, discussions, and MATLAB
programs for computation. It emphasizes details of the relevance of the
material, intuition, and discussions with a view towards very modern
statistical inference. In addition to classic subjects associated with
mathematical statistics, topics include an intuitive presentation of the
(single and double) bootstrap for confidence interval calculations,
shrinkage estimation, tail (maximal moment) estimation, and a variety of
methods of point estimation besides maximum likelihood, including use
of characteristic functions, and indirect inference. Practical examples
of all methods are given. Estimation issues associated with the discrete
mixtures of normal distribution, and their solutions, are developed in
detail. Much emphasis throughout is on non-Gaussian distributions,
including details on working with the stable Paretian distribution and
fast calculation of the noncentral Student's t. An entire chapter is
dedicated to optimization, including development of Hessian-based
methods, as well as heuristic/genetic algorithms that do not require
continuity, with MATLAB codes provided.
The book includes both
theory and nontechnical discussions, along with a substantial reference
to the literature, with an emphasis on alternative, more modern
approaches. The recent literature on the misuse of hypothesis testing
and p-values for model selection is discussed, and emphasis is given to
alternative model selection methods, though hypothesis testing of
distributional assumptions is covered in detail, notably for the normal
distribution.
Presented in three parts—Essential Concepts in
Statistics; Further Fundamental Concepts in Statistics; and Additional
Topics—Fundamental Statistical Inference: A Computational Approach
offers comprehensive chapters on: Introducing Point and Interval
Estimation; Goodness of Fit and Hypothesis Testing; Likelihood;
Numerical Optimization; Methods of Point Estimation; Q-Q Plots and
Distribution Testing; Unbiased Point Estimation and Bias Reduction;
Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The
Method of Indirect Inference; and, as an appendix, A Review of
Fundamental Concepts in Probability Theory, the latter to keep the book
self-contained, and giving material on some advanced subjects such as
saddlepoint approximations, expected shortfall in finance, calculation
with the stable Paretian distribution, and convergence theorems and
proofs.
