A Course in Mathematical Statistics

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Academic Press, Mar 12, 1997 - Mathematics - 572 pages
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A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference.

* Contains 25% new material
* Includes the most complete coverage of sufficiency
* Transformation of Random Vectors
* Sufficiency / Completeness / Exponential Families
* Order Statistics
* Elements of Nonparametric Density Estimation
* Analysis of Variance (ANOVA)
* Regression Analysis
* Linear Models

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Chapter 1 Basic Concepts of Set Theory
Chapter 2 Some Probabilistic Concepts and Results
Chapter 3 On Random Variables and Their Distributions
Chapter 4 Distribution Functions Probability Densities and Their Relationship
Chapter 5 Moments of Random VariablesSome Moment and Probability Inequalities
Chapter 6 Characteristic Functions Moment Generating Functions and Related Theorems
Chapter 7 Stochastic Independence with Some Applications
Chapter 8 Basic Limit Theorems
Chapter 15 Confidence RegionsTolerance Intervals
Chapter 16 The General Linear Hypothesis
Chapter 17 Analysis of Variance
Chapter 18 The Multivariate Normal Distribution
Chapter 19 Quadratic Forms
Chapter 20 Nonparametric Inference
Appendix I Topics from Vector and Matrix Algebra
Appendix II Noncentral t X2 and FDistributions

Chapter 9 Transformations of Random Variables and Random Vectors
Chapter 10 Order Statistics and Related Theorems
Chapter 11 Sufficiency and Related Theorems
Chapter 12 Point Estimation
Chapter 13 Testing Hypotheses
Chapter 14 Sequential Procedures
Appendix III Tables
Some Notation and Abbreviations
Answers to Selected Exercises

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About the author (1997)

George G. Roussas earned a B.S. in Mathematics with honors from the University of Athens, Greece, and a Ph.D. in Statistics from the University of California, Berkeley. As of July 2014, he is a Distinguished Professor Emeritus of Statistics at the University of California, Davis. Roussas is the author of five books, the author or co-author of five special volumes, and the author or co-author of dozens of research articles published in leading journals and special volumes. He is a Fellow of the following professional societies: The American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), The Royal Statistical Society (RSS), the American Association for the Advancement of Science (AAAS), and an Elected Member of the International Statistical Institute (ISI); also, he is a Corresponding Member of the Academy of Athens. Roussas was an associate editor of four journals since their inception, and is now a member of the Editorial Board of the journal Statistical Inference for Stochastic Processes. Throughout his career, Roussas served as Dean, Vice President for Academic Affairs, and Chancellor at two universities; also, he served as an Associate Dean at UC-Davis, helping to transform that institution's statistical unit into one of national and international renown. Roussas has been honored with a Festschrift, and he has given featured interviews for the Statistical Science and the Statistical Periscope. He has contributed an obituary to the IMS Bulletin for Professor-Academician David Blackwell of UC-Berkeley, and has been the coordinating editor of an extensive article of contributions for Professor Blackwell, which was published in the Notices of the American Mathematical Society and the Celebratio Mathematica.

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