- Cover
- Series
- Title Page
- Copyright Page
- Dedication
- Preface
- List of Random Variables
- List of Abbreviations
- Chapter 1: Basic Probability Theory
- PART I: THEORY
- 1.1 OPERATIONS ON SETS
- 1.2 ALGEBRA AND σ–FIELDS
- 1.3 PROBABILITY SPACES
- 1.4 CONDITIONAL PROBABILITIES AND INDEPENDENCE
- 1.5 RANDOM VARIABLES AND THEIR DISTRIBUTIONS
- 1.6 THE LEBESGUE AND STIELTJES INTEGRALS
- 1.7 JOINT DISTRIBUTIONS, CONDITIONAL DISTRIBUTIONS AND INDEPENDENCE
- 1.8 MOMENTS AND RELATED FUNCTIONALS
- 1.9 MODES OF CONVERGENCE
- 1.10 WEAK CONVERGENCE
- 1.11 LAWS OF LARGE NUMBERS
- 1.12 CENTRAL LIMIT THEOREM
- 1.13 MISCELLANEOUS RESULTS
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTIONS TO SELECTED PROBLEMS
- Chapter 2: Statistical Distributions
- PART I: THEORY
- 2.1 INTRODUCTORY REMARKS
- 2.2 FAMILIES OF DISCRETE DISTRIBUTIONS
- 2.3 SOME FAMILIES OF CONTINUOUS DISTRIBUTIONS
- 2.4 TRANSFORMATIONS
- 2.5 VARIANCES AND COVARIANCES OF SAMPLE MOMENTS
- 2.6 DISCRETE MULTIVARIATE DISTRIBUTIONS
- 2.7 MULTINORMAL DISTRIBUTIONS
- 2.8 DISTRIBUTIONS OF SYMMETRIC QUADRATIC FORMS OF NORMAL VARIABLES
- 2.9 INDEPENDENCE OF LINEAR AND QUADRATIC FORMS OF NORMAL VARIABLES
- 2.10 THE ORDER STATISTICS
- 2.11 t–DISTRIBUTIONS
- 2.12 F–DISTRIBUTIONS
- 2.13 THE DISTRIBUTION OF THE SAMPLE CORRELATION
- 2.14 EXPONENTIAL TYPE FAMILIES
- 2.15 APPROXIMATING THE DISTRIBUTION OF THE SAMPLE MEAN: EDGEWORTH AND SADDLEPOINT APPROXIMATIONS
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTIONS TO SELECTED PROBLEMS
- Chapter 3: Sufficient Statistics and the Information in Samples
- PART I: THEORY
- 3.1 INTRODUCTION
- 3.2 DEFINITION AND CHARACTERIZATION OF SUFFICIENT STATISTICS
- 3.3 LIKELIHOOD FUNCTIONS AND MINIMAL SUFFICIENT STATISTICS
- 3.4 SUFFICIENT STATISTICS AND EXPONENTIAL TYPE FAMILIES
- 3.5 SUFFICIENCY AND COMPLETENESS
- 3.6 SUFFICIENCY AND ANCILLARITY
- 3.7 INFORMATION FUNCTIONS AND SUFFICIENCY
- 3.8 THE FISHER INFORMATION MATRIX
- 3.9 SENSITIVITY TO CHANGES IN PARAMETERS
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTIONS TO SELECTED PROBLEMS
- Chapter 4: Testing Statistical Hypotheses
- PART I: THEORY
- 4.1 THE GENERAL FRAMEWORK
- 4.2 THE NEYMAN–PEARSON FUNDAMENTAL LEMMA
- 4.3 TESTING ONE–SIDED COMPOSITE HYPOTHESES IN MLR MODELS
- 4.4 TESTING TWO–SIDED HYPOTHESES IN ONE–PARAMETER EXPONENTIAL FAMILIES
- 4.5 TESTING COMPOSITE HYPOTHESES WITH NUISANCE PARAMETERS—UNBIASED TESTS
- 4.6 LIKELIHOOD RATIO TESTS
- 4.7 THE ANALYSIS OF CONTINGENCY TABLES
- 4.8 SEQUENTIAL TESTING OF HYPOTHESES
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTIONS TO SELECTED PROBLEMS
- Chapter 5: Statistical Estimation
- PART I: THEORY
- 5.1 GENERAL DISCUSSION
- 5.2 UNBIASED ESTIMATORS
- 5.3 THE EFFICIENCY OF UNBIASED ESTIMATORS IN REGULAR CASES
- 5.4 BEST LINEAR UNBIASED AND LEAST–SQUARES ESTIMATORS
- 5.5 STABILIZING THE LSE: RIDGE REGRESSIONS
- 5.6 MAXIMUM LIKELIHOOD ESTIMATORS
- 5.7 EQUIVARIANT ESTIMATORS
- 5.8 ESTIMATING EQUATIONS
- 5.9 PRETEST ESTIMATORS
- 5.10 ROBUST ESTIMATION OF THE LOCATION AND SCALE PARAMETERS OF SYMMETRIC DISTRIBUTIONS
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTIONS OF SELECTED PROBLEMS
- Chapter 6: Confidence and Tolerance Intervals
- PART I: THEORY
- 6.1 GENERAL INTRODUCTION
- 6.2 THE CONSTRUCTION OF CONFIDENCE INTERVALS
- 6.3 OPTIMAL CONFIDENCE INTERVALS
- 6.4 TOLERANCE INTERVALS
- 6.5 DISTRIBUTION FREE CONFIDENCE AND TOLERANCE INTERVALS
- 6.6 SIMULTANEOUS CONFIDENCE INTERVALS
- 6.7 TWO–STAGE AND SEQUENTIAL SAMPLING FOR FIXED WIDTH CONFIDENCE INTERVALS
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTION TO SELECTED PROBLEMS
- Chapter 7: Large Sample Theory for Estimation and Testing
- PART I: THEORY
- 7.1 CONSISTENCY OF ESTIMATORS AND TESTS
- 7.2 CONSISTENCY OF THE MLE
- 7.3 ASYMPTOTIC NORMALITY AND EFFICIENCY OF CONSISTENT ESTIMATORS
- 7.4 SECOND–ORDER EFFICIENCY OF BAN ESTIMATORS
- 7.5 LARGE SAMPLE CONFIDENCE INTERVALS
- 7.6 EDGEWORTH AND SADDLEPOINT APPROXIMATIONS TO THE DISTRIBUTION OF THE MLE: ONE–PARAMETER CANONICAL EXPONENTIAL FAMILIES
- 7.7 LARGE SAMPLE TESTS
- 7.8 PITMAN’S ASYMPTOTIC EFFICIENCY OF TESTS
- 7.9 ASYMPTOTIC PROPERTIES OF SAMPLE QUANTILES
- PART II: EXAMPLES
- PART III: PROBLEMS
- PART IV: SOLUTION OF SELECTED PROBLEMS
- Chapter 8: Bayesian Analysis in Testing and Estimation
- Chapter 9: Advanced Topics in Estimation Theory
- Reference
- Author Index
- Subject Index
- Wiley Series in Probability and Statistics
To my wife Hanna,
our sons Yuval and David,
and their families, with love.
-
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