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
Notions of Probability
Expectations of Functions of Random Variables
Multivariate Random Variables
Transformations and Sampling Distributions
Notions of Stochastic Convergence
Sufficiency, Completeness, and Ancillarity
Tests of Hypotheses
Confidence Interval Estimation
Likelihood Ratio and Other Tests
Sample Size Determination: Two-Stage Procedures
"...the book contains unique features throughout. Examples are the moment problem, which is clarified through a nice example, the role of the probability generating functions, and the central limit theorem for the sample variance. Techniques and concepts are typically illustrated through a series of examples. Within a box is routinely summarized what it is that has been accomplished or where to go from that point. At the end of each chapter a long list of exercises is arranged according the sections. "
---Zentralblatt fur Mathematik, 2000
"…a marvelous book for students."
"…a handy reference as well as a good textbook."
-International Statistical Institute, Short Book Reviews
||September 28, 2016
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