Contents
Chapter 1: Basic Probability Theory
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
PART IV: SOLUTIONS TO SELECTED PROBLEMS
Chapter 2: Statistical Distributions
2.2 FAMILIES OF DISCRETE DISTRIBUTIONS
2.3 SOME FAMILIES OF CONTINUOUS DISTRIBUTIONS
2.5 VARIANCES AND COVARIANCES OF SAMPLE MOMENTS
2.6 DISCRETE MULTIVARIATE DISTRIBUTIONS
2.8 DISTRIBUTIONS OF SYMMETRIC QUADRATIC FORMS OF NORMAL VARIABLES
2.9 INDEPENDENCE OF LINEAR AND QUADRATIC FORMS OF NORMAL VARIABLES
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 IV: SOLUTIONS TO SELECTED PROBLEMS
Chapter 3: Sufficient Statistics and the Information in Samples
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 IV: SOLUTIONS TO SELECTED PROBLEMS
Chapter 4: Testing Statistical Hypotheses
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
4.7 THE ANALYSIS OF CONTINGENCY TABLES
4.8 SEQUENTIAL TESTING OF HYPOTHESES
PART IV: SOLUTIONS TO SELECTED PROBLEMS
Chapter 5: Statistical Estimation
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
5.10 ROBUST ESTIMATION OF THE LOCATION AND SCALE PARAMETERS OF SYMMETRIC DISTRIBUTIONS
PART IV: SOLUTIONS OF SELECTED PROBLEMS
Chapter 6: Confidence and Tolerance Intervals
6.2 THE CONSTRUCTION OF CONFIDENCE INTERVALS
6.3 OPTIMAL CONFIDENCE 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 IV: SOLUTION TO SELECTED PROBLEMS
Chapter 7: Large Sample Theory for Estimation and Testing
7.1 CONSISTENCY OF ESTIMATORS AND TESTS
7.3 ASYMPTOTIC NORMALITY AND EFFICIENCY OF CONSISTENT ESTIMATORS
7.4 SECOND–ORDER EFFICIENCY OF BAN ESTIMATORS
7.5 LARGE SAMPLE CONFIDENCE INTERVALS
7.8 PITMAN’S ASYMPTOTIC EFFICIENCY OF TESTS
7.9 ASYMPTOTIC PROPERTIES OF SAMPLE QUANTILES
PART IV: SOLUTION OF SELECTED PROBLEMS
Chapter 8: Bayesian Analysis in Testing and Estimation
8.2 BAYESIAN TESTING OF HYPOTHESIS
8.3 BAYESIAN CREDIBILITY AND PREDICTION INTERVALS
8.6 EMPIRICAL BAYES ESTIMATORS
PART IV: SOLUTIONS OF SELECTED PROBLEMS
Chapter 9: Advanced Topics in Estimation Theory
9.2 MINIMUM RISK EQUIVARIANT, BAYES EQUIVARIANT, AND STRUCTURAL ESTIMATORS
9.3 THE ADMISSIBILITY OF ESTIMATORS