Mathematical Statistics: Basic Ideas and Selected Topics, Volume 1We 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. |
Contents
STATISTICAL MODELS GOALS AND PERFORMANCE CRITERIA | 1 |
METHODS OF ESTIMATION | 99 |
MEASURES OF PERFORMANCE | 161 |
Copyright | |
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Other editions - View all
Mathematical Statistics: Basic Ideas and Selected Topics, Volume 1 Peter J. Bickel,Kjell A. Doksum No preview available - 2015 |
Mathematical Statistics: Basic Ideas and Selected Topics, Volume 1 Peter J. Bickel,Kjell A. Doksum No preview available - 2007 |
Common terms and phrases
algorithm approximation assumptions asymptotic B₁ Bayes estimate Bayesian Bernoulli trials binomial canonical exponential family compute conditional distribution confidence bounds confidence interval confidence region continuous convergence covariate critical value defined denote density distribution function equation equivalent error Example exists exponential family finite follows frequency function Gaussian given Hint hypothesis independent inequality Let X1 likelihood ratio test linear model log p(x loss function matrix mean method method of moments minimax MSPE multinomial n₁ normal distribution Note observations obtain parameter population posterior distribution predictor prior probability Problems for Section Proof quantile random variables random vector regression rejects H result risk sample Show Slutsky's theorem sufficient statistic Suppose X1 test statistic testing H Theorem theory UMVU unbiased unique variance versus X₁ Xn are i.i.d. Y₁ Z₁ σ²