Introductory Statistical Inference

About this book

This gracefully organized text reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, figures, tables, and computer simulations to develop and illustrate concepts. Drills and boxed summaries emphasize and reinforce important ideas and special techniques.

Beginning with a review of the basic concepts and methods in probability theory, moments, and moment generating functions, the author moves to more intricate topics. Introductory Statistical Inference studies multivariate random variables, exponential families of distributions, and standard probability inequalities. It develops the Helmert transformation for normal distributions, introduces the notions of convergence, and spotlights the central limit theorems. Coverage highlights sampling distributions, Basu's theorem, Rao-Blackwellization and the Cramequality. The o provides in-depth coverage of Lehmann-Scheffe theorems, focuses on tests of hypotheses, describes Bayesian methods and the Bayes' estimator, and develops large-sample inference. The author provides a historical context for statistics and statistical discoveries and answers to a majority of the end-of-chapter exercises.

Designed primarily for a one-semester, first-year graduate course in probability and statistical inference, this text serves readers from varied backgrounds, ranging from engineering, economics, agriculture, and bioscience to finance, financial mathematics, operations and information management, and psychology.

Contents

Probability and DistributionsIntroductionAbout SetsAxiomatic Development of ProbabilityConditional Probability and Independent EventsDiscrete Random VariablesContinuous Random VariablesSome Useful DistributionsExercises and ComplementsMoments and Generating FunctionsIntroductionExpectation and VarianceMoments and Moment Generating FunctionDetermination of a Distribution via MGFProbability Generating FunctionExercises and ComplementsMultivariate Random VariablesIntroductionProbability DistributionsCovariances and Correlation CoefficientIndependence of Random VariablesBivariate Normal DistributionCorrelation Coefficient and IndependenceExponential FamilySelected Probability InequalitiesExercises and ComplementsSampling DistributionIntroductionMoment Generating Function ApproachOrder StatisticsTransformationSpecial Sampling DistributionsMultivariate Normal DistributionSelected Reviews in MatricesExercises and ComplementsNotions of ConvergenceIntroductionConvergence in ProbabilityConvergence in DistributionConvergence of Chi-Square, t, and F distributionsExercises and ComplementsSufficiency, Completeness, and AncillarityIntroductionSufficiencyMinimal SufficiencyInformationAncillarityCompletenessExercises and ComplementsPoint EstimationIntroductionMaximum Likelihood EstimatorCriteria to Compare EstimatorsImproved Unbiased Estimators via SufficiencyUniformly Minimum Variance Unbiased EstimatorConsistent EstimatorExercises and ComplementsTests of HypothesesIntroductionError Probabilities and Power FunctionSimple Null vs. Simple AlternativeOne-Sided Composite AlternativeSimple Null vs. Two-Sided AlternativeExercises and ComplementsConfidence IntervalsIntroductionOne-Sample ProblemsTwo-Sample ProblemsExercises and ComplementsBayesian MethodsIntroductionPrior and Posterior DistributionsConjugate PriorPoint EstimationExamples with a Nonconjugate PriorExercises and ComplementsLikelihood Ratio and Other TestsIntroductionOne-Sample LR Tests: NormalTwo-Sample LR Tests: Independent NormalBivariate NormalExercises and ComplementsLarge-Sample MethodsIntroductionMaximum Likelihood EstimationAsymptotic Relative EfficiencyConfidence Intervals and Tests of HypothesesVariance Stabilizing TransformationExercises and ComplementsAbbreviations, Historical Notes, and TablesAbbreviations and NotationsHistorical NotesSelected Statistical TablesReferencesAnswers: Selected ExercisesAuthor IndexSubject Index

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