Statistical Inference

Pretty solid textbook overall. Pros: 1. Thorough introduction to classical statistics. This text hits most of the major topics in frequentist statistics. 2. Clear exposition, at least in the first 7 chapters. 3. Good selection and variety of problems. See below. Cons: 1. Some important topics are omitted. One that comes to mind is the Multivariate Normal Distribution. A little more Bayesian material would have been nice. Also, some other topics could very well have been omitted which are fairly non standard (ie Union Intersection tests.) 2. Chapters 8-10 are not nearly as strong as the previous chapters. I often had to turn to other sources for additional examples and explanations. 3. Some problems are a complete waste of time. This is my biggest gripe with an otherwise great textbook. Too many problems require drawn out, extremely tedious calculations. Others require leaps of intuition which even seasoned statisticians would not make. My advice is to ask someone who has gone through the problems for recommendations. Or, if a problem is taking a very long time, take a look at the first few lines of the solution - you may save yourself a lot of wasted time. George Casella and Roger L. Berger's new edition builds the theoretical statistics from the first principals of probability theory. Thoroughly and completely, the authors start with the basics of probability and then move on to develop the theory of statistical inference using techniques, definitions, and statistical concepts.-- Restructures some material to provide better ordering of topics in Chapters 3-11.-- Provides updated and expanded Exercises and Miscellanea in all chapters.-- Includes strong coverage of topics such as ancillary, invariance, Bayesian methods, pivots, Stein estimation, and errors in variables and inequalities.-- Includes a thorough introduction to decision theory that features the most modern material available.-- Separates the finding of appropriate statistical techniques and the methods of evaluating these techniques. This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. This book can be used for readers who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations. Probability Theory -- Transformations And Expectations -- Common Families Of Distributions -- Multiple Random Variables -- Properties Of A Random Sample -- Principles Of Data Reduction -- Point Estimation -- Hypothesis Testing -- Interval Estimation -- Asymptotic Evaluations -- Analysis Of Variance And Regression -- Regression Models. George Casella, Roger L. Berger. Includes Bibliographical References (p. [629]-644) And Indexes. Probability Theory Transformations and Expectations Common Families of Distributions Multiple Random Variables Properties of a Random Sample Principles of Data Retention Point Estimation Hypothesis Testing Interval Estimation Asymptotic Evaluations Analysis of Variance and Regression Regression Models Appendix: Computer Algebra Table of Common Distributions References Author Index Subject Index The subject of probability theory is the foundation upon which all of statistics is built, providing a means for modeling populations, experiments, or almost anything else that could be considered a random phenomenon.