Statistics in the Health Sciences : Theory, Applications, and Computing

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Content: Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface Authors Chapter 1: Prelude: Preliminary Tools and Foundations 1.1 Introduction 1.2 Limits 1.3 Random Variables 1.4 Probability Distributions 1.5 Commonly Used Parametric Distribution Functions 1.6 Expectation and Integration 1.7 Basic Modes of Convergence of a Sequence of Random Variables 1.7.1 Convergence in Probability 1.7.2 Almost Sure Convergence 1.7.3 Convergence in Distribution 1.7.4 Convergence in rth Mean 1.7.5 O(.) and o(.) Revised under Stochastic Regimes 1.7.6 Basic Associations between the Modes of Convergence1.8 Indicator Functions and Their Bounds as Applied to Simple Proofs of Propositions 1.9 Taylorâ#x80 #x99 s Theorem 1.10 Complex Variables 1.11 Statistical Software: R and SAS 1.11.1 R Software 1.11.2 SAS Software Chapter 2: Characteristic Functionâ#x80 #x93 Based Inference 2.1 Introduction 2.2 Elementary Properties of Characteristic Functions 2.3 One-to-One Mapping 2.3.1 Proof of the Inversion Theorem 2.4 Applications 2.4.1 Expected Lengths of Random Stopping Times and Renewal Functions in Light of Tauberian Theorems 2.4.2 Risk-Efficient Estimation2.4.3 Khinchinâ#x80 #x99 s (or Hinchinâ#x80 #x99 s) Form of the Law of Large Numbers 2.4.4 Analytical Forms of Distribution Functions 2.4.5 Central Limit Theorem 2.4.5.1 Principles of Monte Carlo Simulations 2.4.5.2 That Is the Question: Do Convergence Rates Matter? 2.4.6 Problems of Reconstructing the General Distribution Based on the Distribution of Some Statistics 2.4.7 Extensions and Estimations of Families of Distribution Functions Chapter 3: Likelihood Tenet 3.1 Introduction 3.2 Why Likelihood? An Intuitive Point of View 3.3 Maximum Likelihood Estimation 3.4 The Likelihood Ratio3.5 The Intrinsic Relationship between the Likelihood Ratio Test Statistic and the Likelihood Ratio of Test Statistics: One More Reason to Use Likelihood 3.6 Maximum Likelihood Ratio 3.7 An Example of Correct Model-Based Likelihood Formation Chapter 4: Martingale Type Statistics and Their Applications 4.1 Introduction 4.2 Terminology 4.3 The Optional Stopping Theorem and Its Corollaries: Waldâ#x80 #x99 s Lemma and Doobâ#x80 #x99 s Inequality 4.4 Applications 4.4.1 The Martingale Principle for Testing Statistical Hypotheses 4.4.1.1 Maximum Likelihood Ratio in Light of the Martingale Concept4.4.1.2 Likelihood Ratios Based on Representative Values 4.4.2 Guaranteed Type I Error Rate Control of the Likelihood Ratio Tests 4.4.3 Retrospective Change Point Detection Policies 4.4.3.1 The Cumulative Sum (CUSUM) Technique 4.4.3.2 The Shiryayevâ#x80 #x93 Roberts (SR) Statistic-Based Techniques 4.4.4 Adaptive (Nonanticipating) Maximum Likelihood Estimation 4.4.5 Sequential Change Point Detection Policies 4.5 Transformation of Change Point Detection Methods into a Shiryayevâ#x80 #x93 Roberts Form 4.5.1 Motivation 4.5.2 The Method 4.5.3 CUSUM versus Shiryayevâ#x80 #x93 Roberts