Li B., Babu G.J. A Graduate Course on Statistical Inference

Springer, 2019. — 386 p. — (Springer Texts in Statistics). — ISBN: 978-1-4939-9759-6.This textbook offers an accessible and comprehensive overview of statistical estimation and inference that reflects current trends in statistical research. It draws from three main themes throughout: the finite-sample theory, the asymptotic theory, and Bayesian statistics. The authors have included a chapter on estimating equations as a means to unify a range of useful methodologies, including generalized linear models, generalized estimation equations, quasi-likelihood estimation, and conditional inference. They also utilize a standardized set of assumptions and tools throughout, imposing regular conditions and resulting in a more coherent and cohesive volume. Written for the graduate-level audience, this text can be used in a one-semester or two-semester course.Probability and Random Variables
Classical Theory of Estimation
Testing Hypotheses for a Single Parameter
Testing Hypotheses in the Presence of Nuisance Parameters
Basic Ideas of Bayesian Methods
Bayesian Inference
Asymptotic tools and projections
Asymptotic theory for Maximum Likelihood Estimation
Estimating equations
Convolution Theorem and Asymptotic Efficiency
Asymptotic Hypothesis Test