Mathematical Statistics: Basic Ideas and Selected Topics, Volume 1
We now have an updated printing! Find more information at: http://vig.prenhall.com/catalog/academic/product/0,1144,0132306379,00.html. In response to feedback from faculty and students, some sections within the book have been rewritten. Also, a number of corrections have been made, further improving the accuracy of this outstanding textbook. This classic, time-honored introduction to the theory and practice of statistics modeling and inference reflects the changing focus of contemporary Statistics. Coverage begins with the more general nonparametric point of view and then looks at parametric models as submodels of the nonparametric ones which can be described smoothly by Euclidean parameters. Although some computational issues are discussed, this is very much a book on theory. It relates theory to conceptual and technical issues encountered in practice, viewing theory as suggestive for practice, not prescriptive. It shows readers how assumptions which lead to neat theory may be unrealistic in practice. Statistical Models, Goals, and Performance Criteria. Methods of Estimation. Measures of Performance, Notions of Optimality, and Construction of Optimal Procedures in Simple Situations. Testing Statistical Hypotheses: Basic Theory. Asymptotic Approximations. Multiparameter Estimation, Testing and Confidence Regions. A Review of Basic Probability Theory. More Advanced Topics in Analysis and Probability. Matrix Algebra. For anyone interested in mathematical statistics working in statistics, bio-statistics, economics, computer science, and mathematics.
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STATISTICAL MODELS GOALS AND PERFORMANCE CRITERIA
METHODS OF ESTIMATION
MEASURES OF PERFORMANCE
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algorithm approximation assume assumptions asymptotic Bayes estimate Bayes procedures Bayes rule Bayesian Bernoulli trials binomial bivariate normal called canonical exponential family Chapter coefficient compute conditional distribution confidence interval confidence region continuous convergence convex Corollary corresponding covariate critical value defined denote density discrete distribution function equation equivalent error Example exists exponential family finite follows frequency function given Hint identically distributed independent inequality instance least squares Let Xi likelihood ratio test linear model loss function matrix maximum likelihood estimates mean median method of moments minimax minimizes MSPE multinomial noncentral normal distribution observations obtain optimal parameter plug-in estimate population posterior distribution prediction prediction interval probability Problems for Section Proof quantile random variables random vector regression rejects H result sample Show Slutsky's theorem sufficient statistic Suppose test statistic testing H Theorem theory UMVU unique versus Xn are i.i.d.