1 Mathematical Background 1
1.1 The concept of limit 2
1.2 Embedding sequences 8
1.3 Infinite series 13
1.4 Order relations and rates of convergence 18
1.5 Continuity 26
1.6 Distributions 30
1.7 Problems 34
2 Convergence in Probability and in Law 47
2.1 Convergence in probability 47
2.2 Applications 55
2.3 Convergence in law 63
2.4 The central limit theorem 72
2.5 Taylor's theorem and the delta method 85
2.6 Uniform convergence 93
2.7 The CLT for independent non-identical random variables 97
2.8 Central limit theorem for dependent variables 106
2.9 Problems 119
3 Performance of Statistical Tests 133
3.1 Critical values 133
3.2 Comparing two treatments 146
3.3 Power and sample size 158
3.4 Comparison oftests:Relative efficiency 173
3.5 Robustness 187
3.6 Problems 202
4 Estimation 219
4.1 Confidence intervals 219
4.2 Accuracy of point estimators 232
4.3 Comparing estimators 239
4.4 Sampling from a finite population 253
4.5 Problems 269
5 Multivariate Extensions 277
5.1 Convergence ofmultivariate distributions 277
5.2 The bivariate normal distribution 287
5.3 Some linear algebra 300
5.4 The multivariate normal distribution 309
5.5 Some applications 319
5.6 Estimation and testing in 2×2 tables 330
5.7 Testing goodness of fit 335
5.8 Problems 349
6 Nonparametric Estimation 363
6.1 U-Statistics 364
6.2 Statistical functionals 381
6.3 Limit distributions of statistical functionals 393
6.4 Density estimation 406
6.5 Bootstrapping 420
6.6 Problems 435
7 Efficient Estimators and Tests 451
7.1 Maximum likelihood 452
7.2 Fisher information 462
7.3 Asymptotic normality and multiple roots 469
7.4 Efficiency 484
7.5 The multiparameter case Ⅰ．Asymptotic normality 497
7.6 The multiparameter case Ⅱ．Efficiency 509
7.7 Tests and confidence intervals 525
7.8 Contingency tables 541
7.9 Problems 551
Appendix 571
References 591
Author Index 609
Subject Index 615