大样本理论基础(英文版)
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作者(美)E.L.莱曼
出版社世界图书出版公司
ISBN9787519220778
出版时间2017-07
装帧其他
开本其他
定价95元
货号3872661
上书时间2024-10-17
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目录
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 functionais
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 norrnality
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
内容摘要
E.L.莱曼著的《大样本理论基础》是一部全面论述一阶大样本理论的经典教科书，是世界各国公认的统计专业研究生的首选教材。书中讨论了大量的应用问题，包括密度估计、自助法和抽样方法论的渐进。
本书内容深入浅出，学习者只需掌握微积分基础知识。各章最后有问题和练习，每节末有小结。
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