A Graduate Course on Statistical Inference

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.

Autorentext

Bing Li is Verne M. Wallaman Professor of Statistics at Pennsylvania State University. He is the author of Sufficient Dimension Reduction: Methods and Applications with R (2018). Dr. Li has served as an associate editor for The Annals of Statistics and is currently serving as an associate editor for Journal of the American Association. G. Jogesh Babu is a distinguished professor of statistics, astronomy, and astrophysics, as well as director of the Center for Astrostatistics, at Pennsylvania State University. He was the 2018 winner of the Jerome Sacks Award for Cross-Disciplinary Research. He and his colleague Dr. E.D. Feigelson coined the term "astrostatistics," when they co-authored a book by the same name in 1996. Dr. Babu's numerous publications also include Statistical Challenges in Modern Astronomy V (with Feigelson, Springer 2012) and Modern Statistical Methods for Astronomy with R Applications (2012).

Inhalt

1. Probability and Random Variables.- 2. Classical Theory of Estimation.- 3. Testing Hypotheses in the Presence of Nuisance Parameters.- 4. Testing Hypotheses in the Presence of Nuisance Parameters.- 5. Basic Ideas of Bayesian Methods.- 6. Bayesian Inference.- 7. Asymptotic Tools and Projections.- 8. Asymptotic Theory for Maximum Likelihood Estimation.- 9. Estimating Equations.- 10. Convolution Theorem and Asymptotic Efficiency.- 11. Asymptotic Hypothesis Test.- References.- Index.