Probability and Statistical Inference

✍ Scribed by Nitis Mukhopadhyay

• Publisher: CRC Press
• Year: 2000
• Tongue: English
• Leaves: 690
• Series: Statistics: A Series of Textbooks and Monographs
• Edition: 1
• Category: Library

✦ Synopsis

Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning with an introduction to the basic ideas and techniques in probability theory and progressing to more rigorous topics, Probability and Statistical Inference

studies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributions

develops notions of convergence in probability and distribution

spotlights the central limit theorem (CLT) for the sample variance

introduces sampling distributions and the Cornish-Fisher expansions

concentrates on the fundamentals of sufficiency, information, completeness, and ancillarity

explains Basu's Theorem as well as location, scale, and location-scale families of distributions

covers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequality

discusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theorems

focuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervals

includes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficient

summarizes Bayesian methods

describes the monotone likelihood ratio (MLR) property

handles variance stabilizing transformations

provides a historical context for statistics and statistical discoveries

showcases great statisticians through biographical notes Employing over 1400 equations to reinforce its subject matter, Probability and Statistical Inference is a groundbreaking text for first-year graduate and upper-level undergraduate courses in probability and statistical inference who have completed a calculus prerequisite, as well as a supplemental text for classes in Advanced Statistical Inference or Decision Theory.

✦ Table of Contents

Contents......Page 20
1 Notions of Probability......Page 26
2 Expectations of Functions of Random Variables......Page 90
3 Multivariate Random Variables......Page 124
4 Functions of Random Variables and Sampling Distribution......Page 202
5 Concepts of Stochastic Convergence......Page 266
6 Sufficiency, Completeness, and Ancillarity......Page 306
7 Point Estimation......Page 366
8 Tests of Hypotheses......Page 420
9 Confidence Interval Estimation......Page 466
10 Bayesian Methods......Page 502
11 Likelihood Ratio and Other Tests......Page 532
12 Large-Sample Inference......Page 564
13 Sample Size Determination: Two-Stage Procedures......Page 594
14 Appendix......Page 616
Index......Page 674