Theory of Statistical Inference

Theory of Statistical Inference is a comprehensive textbook on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of foundational ideas, emphasizes the application of mathematical theory, and covers topics such as distribution theory, statistical inference, estimation, confidence intervals, hypothesis testing, large sample theory, and equation methods. The book also includes treatment of linear and nonlinear regression models, ANOVA models, GLM, and GEE, and emphasizes the importance of decision theory and group theory in statistical inference.

Format: Hardback
Length: 457 pages
Publication date: 22 December 2021
Publisher: Taylor & Francis Ltd

Theory of Statistical Inference is a comprehensive reference designed for researchers and students pursuing advanced studies in statistics or biostatistics. It offers a unified treatment of foundational ideas in modern statistical inference, making it suitable for a core course in graduate programs in these fields. The book emphasizes the application of mathematical theory to the problem of inference, leading to an optimization theory that enables the selection of statistical methods that maximize the utilization of data.

The volume is organized into four sections:

Part I provides a review of the necessary distribution theory, which forms the foundation for statistical inference.

Part II introduces the concept of statistical inference, encompassing definitions such as the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals, and hypothesis testing are introduced in this section.

Part III constitutes the core of the volume, presenting a formal theory of statistical inference. It begins with decision theory and covers topics such as uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation, and the Neyman-Pearson test. Additionally, Part III explores large sample theory, including stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound, and asymptotic efficiency. A separate chapter is dedicated to estimating equation methods.

The volume concludes with a detailed development of large sample hypothesis testing, based on the likelihood ratio.

Theory of Statistical Inference is an essential resource for anyone seeking to deepen their understanding of statistical inference and its applications in research and practice. Its comprehensive coverage, rigorous mathematical approach, and practical examples make it a valuable tool for both novice and experienced researchers in the field.

Weight: 1116g
Dimension: 184 x 260 x 35 (mm)
ISBN-13: 9780367488758