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.
"…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."
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.