Statistical theory: a concise introduction

Introduction Preamble Likelihood Sufficiency Minimal sufficiency Completeness Exponential family of distributionsPoint Estimation Introduction Maximum likelihood estimation Method of moments Method of least squares Goodness-of-estimation. Mean squared error. Unbiased estimationConfidence Intervals, Bounds, and Regions Introduction Quoting the estimation error Confidence intervalsConfidence bounds Confidence regionsHypothesis Testing Introduction Simple hypothesesComposite hypothesesHypothesis testing and confidence intervals Sequential testingAsymptotic Analysis Introduction Convergence and consistency in MSE Convergence and consistency in probability Convergence in distribution The central limit theorem Asymptotically normal consistency Asymptotic confidence intervals Asymptotic normality of the MLE Multiparameter case Asymptotic distribution of the GLRT. Wilks' theorem.Bayesian Inference Introduction Choice of priors Point estimation Interval estimation. Credible sets. Hypothesis testingElements of Statistical Decision Theory Introduction and notations Risk function and admissibility Minimax risk and minimax rules Bayes risk and Bayes rules Posterior expected loss and Bayes actions Admissibility and minimaxity of Bayes rules Linear ModelsIntroduction Definition and examples Estimation of regression coefficients Residuals. Estimation of the variance. Examples Goodness-of-fit. Multiple correlation coefficient. Confidence intervals and regions for the coefficients Hypothesis testing in linear models Predictions Analysis of varianceAppendix A: Probabilistic ReviewAppendix B: Solutions of Selected ExercisesIndexExercises appear at the end of each chapter.