Preface 1 Mathematical Background 1.1 The concept of limit 1.2 Embedding sequences 1.3 Infinite series 1.4 Order relations and rates of convergence 1.5 Continuity 1.6 Distributions 1.7 Problems 2 Convergence in Probability and in Law 2.1 Convergence in probability 2.2 Applications 2.3 Convergence in law 2.4 The central limit theorem 2.5 Taylor's theorem and the delta method 2.6 Uniform convergence 2.7 The CLT for independent non-identical random variables 2.8 Central limit theorem for dependent variables 2.9 Problems 3 Performance of Statistical Tests 3.1 Critical values 3.2 Comparing two treatments 3.3 Power and sample size 3.4 Comparison of tests: Relative efficiency 3.5 Robustness 3.6 Problems 4 Estimation 4.1 Confidence intervals 4.2 Accuracy of point estimators 4.3 Comparing estimators 4.4 Sampling from a finite population 4.5 Problems 5 Multivariate Extensions 5.1 Convergence of multivariate distributions 5.2 The bivariate normal distribution 5.3 Some linear algebra 5.4 The multivariate normal distribution 5.5 Some applications 5.6 Estimation and testing in 2 × 2 tables 5.7 Testing goodness of fit 5.8 Problems 6 Nonparametric Estimation 6.1 U-Statistics 6.2 Statistical functionals 6.3 Limit distributions of statistical functionals 6.4 Density estimation 6.5 Bootstrapping 6.6 Problems 7 Efficient Estimators and Tests 7.1 Maximum likelihood 7.2 Fisher information 7.3 Asymptotic normality and multiple roots 7.4 Efficiency 7.5 The multiparameter case I. Asymptotic normality 7.6 The multiparameter case II. Efficiency 7.7 Tests and confidence intervals 7.8 Contingency tables 7.9 Problems Appendix References Author Index Subject Index
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