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大样本理论基础 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- (美)E.L.莱曼著 著
- 出版社: 北京;西安:世界图书出版公司
- ISBN:751922077X
- 出版时间:2016
- 标注页数:632页
- 文件大小:90MB
- 文件页数:645页
- 主题词:样本调查(统计学)-英文
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图书目录
1 Mathematical Background1
1.1 The concept of limit2
1.2 Embedding sequences8
1.3 Infinite series13
1.4 Order relations and rates of convergence18
1.5 Continuity26
1.6 Distributions30
1.7 Problems34
2 Convergence in Probability and in Law47
2.1 Convergence in probability47
2.2 Applications55
2.3 Convergence in law63
2.4 The central limit theorem72
2.5 Taylor's theorem and the delta method85
2.6 Uniform convergence93
2.7 The CLT for independent non-identical random variables97
2.8 Central limit theorem for dependent variables106
2.9 Problems119
3 Performance of Statistical Tests133
3.1 Critical values133
3.2 Comparing two treatments146
3.3 Power and sample size158
3.4 Comparison oftests:Relative efficiency173
3.5 Robustness187
3.6 Problems202
4 Estimation219
4.1 Confidence intervals219
4.2 Accuracy of point estimators232
4.3 Comparing estimators239
4.4 Sampling from a finite population253
4.5 Problems269
5 Multivariate Extensions277
5.1 Convergence ofmultivariate distributions277
5.2 The bivariate normal distribution287
5.3 Some linear algebra300
5.4 The multivariate normal distribution309
5.5 Some applications319
5.6 Estimation and testing in 2×2 tables330
5.7 Testing goodness of fit335
5.8 Problems349
6 Nonparametric Estimation363
6.1 U-Statistics364
6.2 Statistical functionals381
6.3 Limit distributions of statistical functionals393
6.4 Density estimation406
6.5 Bootstrapping420
6.6 Problems435
7 Efficient Estimators and Tests451
7.1 Maximum likelihood452
7.2 Fisher information462
7.3 Asymptotic normality and multiple roots469
7.4 Efficiency484
7.5 The multiparameter case Ⅰ.Asymptotic normality497
7.6 The multiparameter case Ⅱ.Efficiency509
7.7 Tests and confidence intervals525
7.8 Contingency tables541
7.9 Problems551
Appendix571
References591
Author Index609
Subject Index615