Mathematical Statistics Volume I

For graduatelevel courses in Statistical Inference or Theoretical Statisticsin departments of Statistics BioStatistics Economics Computer Science andMathematics.An updated printing In response to feedback from faculty and students somesections within the book have been rewritten. Also a number of correctionshave been made further improving the accuracy of this outstanding textbook.This updated classic timehonored introduction to the theory and practice ofstatistics modeling and inference reflects the changing focus of contemporaryStatistics. Coverage begins with the more general nonparametric point of viewand then looks at parametric models as submodels of the nonparametric oneswhich can be described smoothly by Euclidean parameters. Although somecomputational issues are discussed this is very much a book on theory. Itrelates theory to conceptual and technical issues encountered in practiceviewing theory as suggestive for practice not prescriptive. It shows readershow 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 OptimalProcedures in Simple Situations. Testing Statistical Hypotheses Basic Theory.Asymptotic Approximations. Multiparameter Estimation Testing and ConfidenceRegions. A Review of Basic Probability Theory. More Advanced Topics in Analysisand Probability. Matrix Algebra.