Statistical Inference

by George Casella, Roger Berger

Overview

Basics of probability to theory of statistical inference using techniques, definitions, concepts that are statistical, natural extensions, consequences, of previous concepts. Topics from a standard inference course: distributions, random variables, data reduction, point estimation, hypothesis testing, interval estimation, regression.

Product Details

ISBN-13:	9781032593036
Publisher:	CRC Press
Publication date:	05/23/2024
Series:	Chapman & Hall/CRC Texts in Statistical Science
Edition description:	2nd ed.
Pages:	565
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

Professor George Casella completed his undergraduate education at Fordham University and graduate education at Purdue University. He served on the faculty of Rutgers University, Cornell University, and the University of Florida. His contributions focused on the area of statistics including Monte Carlo methods, model selection, and genomic analysis. He was particularly active in Bayesian and empirical Bayes methods, with works connecting with the Stein phenomenon, on assessing and accelerating the convergence of Markov chain Monte Carlo methods, as in his Rao-Blackwellisation technique, and recasting lasso as Bayesian posterior mode estimation with independent Laplace priors.

Casella was named as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics in 1988, and he was made an Elected Fellow of the International Statistical Institute in 1989. In 2009, he was made a Foreign Member of the Spanish Royal Academy of Sciences.

After receiving his doctorate in statistics from Purdue University, Professor Roger Berger held academic positions at Florida State University and North Carolina State University. He also spent two years with the National Science Foundation before coming to Arizona State University in 2004. Berger is co-author of the textbook "Statistical Inference," now in its second edition. This book has been translated into Chinese and Portuguese. His articles have appeared in publications including Journal of the American Statistical Association, Statistical Science, Biometrics and Statistical Methods in Medical Research. Berger's areas of expertise include hypothesis testing, (bio)equivalence, generalized linear models, biostatistics, and statistics education.

Berger was named as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.

Table of Contents

1. PROBABILITY THEORY. Set Theory. Probability Theory. Conditional Probability and Independence. Random Variables. Distribution Functions. Density and Mass Functions. Exercises. Miscellanea. 2. TRANSFORMATION AND EXPECTATIONS. Distribution of Functions of a Random Variable. Expected Values. Moments and Moment Generating Functions. Differentiating Under an Integral Sign. Exercises. Miscellanea. 3. COMMON FAMILIES OF DISTRIBUTIONS. Introductions. Discrete Distributions. Continuous Distributions. Exponential Families. Locations and Scale Families. Inequalities and Identities. Exercises. Miscellanea. 4. MULTIPLE RANDOM VARIABLES. Joint and Marginal Distributions. Conditional Distributions and Independence. Bivariate Transformations. Hierarchical Models and Mixture Distributions. Covariance and Correlation. Multivariate Distributions. Inequalities. Exercises. Miscellanea. 5. PROPERTIES OF A RANDOM SAMPLE. Basic Concepts of Random Samples. Sums of Random Variables from a Random Sample. Sampling for the Normal Distribution. Order Statistics. Convergence Concepts. Generating a Random Sample. Exercises. Miscellanea. 6. PRINCIPLES OF DATA REDUCTION. Introduction. The Sufficiency Principle. The Likelihood Principle. The Equivariance Principle. Exercises. Miscellanea. 7. POINT EXTIMATION. Introduction. Methods of Finding Estimators. Methods of Evaluating Estimators. Exercises. Miscellanea. 8. HYPOTHESIS TESTING. Introduction. Methods of Finding Tests. Methods of Evaluating Test. Exercises. Miscellanea. 9. INTERVAL ESTIMATION. Introduction. Methods of Finding Interval Estimators. Methods of Evaluating Interval Estimators. Exercises. Miscellanea. 10. ASYMPTOTIC EVALUATIONS. Point Estimation. Robustness.Hypothesis Testing. Interval Estimation. Exercises. Miscellanea. 11. ANALYSIS OF VARIANCE AND REGRESSION. Introduction. One-way Analysis of Variance. Simple Linear Regression. Exercises. Miscellanea. 12. REGRESSION MODELS. Introduction. Regression with Errors in Variables. Logistic Regression. Robust Regression. Exercises. Miscellanea. Appendix. Computer Algebra. References.