Mathematical Statistics

Mathematical Statistics

  • Electronic book text
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Description

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology.The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.show more

Product details

  • Electronic book text | 504 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 1000 equations; 14 Tables, black and white
  • 1584888563
  • 9781584888567

Table of contents

INTRODUCTION TO PROBABILITYRandom ExperimentsProbability MeasuresConditional Probability and IndependenceRandom VariablesExpected ValuesRANDOM VECTORS AND JOINT DISTRIBUTIONSIntroductionDiscrete and Continuous Random VectorsConditional DistributionsNormal DistributionsPoisson ProcessesGenerating Random VariablesCONVERGENCE OF RANDOM VARIABLESIntroductionConvergence in Probability and DistributionWLLNProving Convergence in DistributionCLTSome ApplicationsConvergence with Probability 1PRINCIPLES OF POINT ESTIMATIONIntroductionStatistical ModelsSufficiencyPoint EstimationSubstitution PrincipleInfluence CurvesStandard ErrorsRelative EfficiencyThe JackknifeLIKELIHOOD-BASED ESTIMATIONIntroductionThe Likelihood FunctionThe Likelihood PrincipleAsymptotics for MLEsMisspecified ModelsNonparametric Maximum Likelihood EstimationNumerical ComputationBayesian EstimationOPTIMAL ESTIMATIONDecision TheoryUMVUEsThe Cramer-Rao Lower BoundAsymptotic EfficiencyINTERVAL ESTIMATION AND HYPOTHESIS TESTINGConfidence Intervals and RegionsHighest Posterior Density RegionsHypothesis TestingLikelihood Ratio TestsOther IssuesLINEAR AND GENERALIZED LINEAR MODELSLinear ModelsEstimationTestingNon-Normal ErrorsGeneralized Linear ModelsQuasi-Likelihood ModelsGOODNESS OF FITIntroductionTests Based on the Multinomial DistributionSmooth Goodness of Fit TestsREFERENCES Each chapter also contains a Problems and Complements sectionshow more