A Course In Mathematical Statistics Pdf

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Description

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.

Key Features

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

Readership

Advanced undergraduate and graduate level courses in mathematical statistics offered in departments of statistics at all major universities. Students in statistics, mathematics, computer science, engineering, life sciences, andsocial sciences may take such a course.

Concepts of Set Theory
Some Probabilistic Concepts and Results
On Random variables and Their Distributions
Distribution Functions, Probability Densities, and their Relationships
Moments of Random Variables-Some Moment and Probability Inequalities
Characteristic Functions, Moment Generating
Functions, and Related Theorems
Stochastic Independence with Some Applications
Basic Limit Theorems
Transformations of Random Variables and Random
Vectors
Order Statistics and Related Theorems
Sufficiency and Related Theorems
Point Estimation
Testing Hypotheses
Sequential Procedures
Confidence Regions-Tolerance Intervals
The General Linear Hypothesis
Analysis of Variance
The Multivariate Normal Distribution
Quadratic Forms
Nonparametric Inference
Appendices
Table of Selected Discrete and Continuous
Distributions and Some of their Characteristics
Some Notation and Abbreviations

Product details

No. of pages: 572

Language: English

Published: February 28, 1997

Imprint: Academic Press

eBook ISBN: 9780080493145

About the Author

George Roussas

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.

Affiliations and Expertise

University of California, Davis, USA