A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistical procedures. Chapters 4 and 5 cover hypothesis testing with simple and null hypotheses, respectively. Subsequent chapters discuss non-parametrics, interval estimation, point estimation, asymptotics, Bayesian procedure, and deviation theory. Student familiarity with standard statistical techniques is assumed.
Table of Contents
Preface. Introduction. Some General Concepts. Pure Significance Tests. Significance Tests: Simple Null Hypotheses. Significance Tests: Composite Null Hypotheses. Distribution-Free and Randomization Tests. Interval Estimation Point Estimation. Asymptotic Theory. Bayesian Methods. Decision Theory. Appendix 1: Determination of Probability Distributions. Appendix 2: Order Statistics. Appendix 3: Second-Order Regression for Arbitrary Random Variables. References. Author Index. Subject Index.
"...the discussion is accessible and thought-provoking. The notes provide good entries to the literature on each chapter's topics as well as a brief historical survey of the topics...The exercises are challenging. Also of special interest are the numerous examples throughout the text."