Problems and Solutions in Theoretical Statistics

In our book Theoretical Statistics we gave about 150 Further results and exercises mostly intended to illustrate material of intrinsic interest that it was not possible to cover in the main text. In many cases the statements were based quite directly on recent papers. The present book gives outline solutions and discussion of these problems. To make the book selfcontained we have preceded each set of problems by a brief summary of the main general ideas required. The collection of these summaries provides a rapid review of the theory of statistics. The book contains a substantial amount of general material not previously available in book form. The detailed solution of special problems is a vital part of the study of any mathematical subject and we hope therefore that teachers and students of statistics especially at graduate level will find the problems and outline solutions helpful. In addition we hope that research workers in statistics interested in special problems will find the book an effective review of some useful theoretical ideas including the associated elementary mathematical techniques. While the numbering and arrangement of the problems is the same as in Theoretical Statistics, we have rewritten a number of the problems, partly in order to make them self contained and partly for clarification and correction.

1. Introduction.- Summary.- 2. Some general concepts.- Summary.- Problems and solutions.- 3. Pure significance tests.- Summary.- Problems and solutions.- 4. Significance tests: simple null hypotheses.- Summary.- Problems and solutions.- 5. Significance tests: composite null hypotheses.- Summary.- Problems and solutions.- 6. Distribution-free and randomization tests.- Summary.- Problems and solutions.- 7. Interval estimation.- Summary.- Problems and solutions.- 8. Point estimation.- Summary.- Problems and solutions.- 9. Asymptotic theory.- Summary.- Problems and solutions.- 10. Bayesian methods.- Summary.- Problems and solutions.- 11. Decision theory.- Summary.- Problems and solutions.- References.- Author Index.