带相依结构的二维列联表的多重比较
发布时间：2021-07-09 20:38
列联表是一种常见的数据存储格式,其中的数据是将观测数据按两个或者更多属性进行分类后的频数。列联表常用于医学、生物学、社会科学等学科之中。通过对列联表进行统计分析,可以考察各个属性之间是否有联系,也就是判断两个属性变量是否具有独立性.可用于检验列联表中的两个属性变量的独立性的假设检验方法有:卡方独立检验、Fisher精确检验、Cochran-Mantel-Haenszel检验[1]等。本文的目的是建立一个模型,进而基于这个模型提出一个新的检验方法,用于检验列联表的属性变量的独立性,这个模型也可以衡量两个属性变量的（正、负）相关性。本文的整体思路是通过引入一个可以衡量变量相关性的参数,构造一个二元二项分布,并将它用于对二维列联表的统计分析。在绪论中,我们总结了文献中已有的二元二项分布。假设随机向量（X,Y）服从二元二项分布,且两个边际分布都是二项分布,即X～Binomial（n1,π2）和Y～Binomial（n2,π2）。文献中已有的二元二项分布大致可以分成三类:第一种是要求n1与n2相等,即n1=n2=n;第二种是要求π1和π2相等,即π1=π2=π;第三种对n1,n2和π1,π2不做...
【文章来源】：哈尔滨工业大学黑龙江省 211工程院校 985工程院校
【文章页数】：70 页
【学位级别】：硕士
【文章目录】：
摘要
Abstract
Chapter 1 Introduction
1.1 Background and Significance
1.2 Literature Review
1.3 Thesis Outline
Chapter 2 A New Bivariate Binomial Model
2.1 Introduction of Model
2.2 Theoretical Properties
2.3 Estimation of Parameters
2.3.1 Maximum Likelihood Estimation
2.3.2 Bootstrap Confidence Interval
2.3.3 Parameter Estimation of Incomplete 2 × 2 Contingency Tables
2.4 Test of independence
2.4.1 Likelihood Ratio Test
2.4.2 Score Test
2.4.3 Wald test
2.4.4 Bootstrap Hypothesis Test
2.4.5 Bartlett-Corrected LRT
2.5 Brief Summary
Chapter 3 Multiple Comparison of Dependency Parameter
3.1 Multiple Comparison Problem
3.2 Controlling Methods for p-value
3.2.1 Bonferroni's Method
3.2.2 Sidak's Method
3.2.3 Holm's Method and Hochberg's Method
3.2.4 Hommel's Method
3.2.5 Benjamini-Hochberg Method and Benjamini-Yekutieli Method
3.3 Resampling Method
3.4 Brief Summary
Chapter 4 Simulation Studies
4.1 Accuracy of Point Estimators and Interval Estimators
4.2 Performance of Three Asymptotic Tests and the Bootstrap Test
4.3 A Real Data Example
4.4 Multiple Comparison
4.5 Brief Summary
Conclusions
结论
References
Appendix A First and Second Partial Derivatives of (2-23)
Appendix B Cumulants and their Derivatives for the Bartlett Correction Factor
Acknowledgements
本文编号：3274456
【文章来源】：哈尔滨工业大学黑龙江省 211工程院校 985工程院校
【文章页数】：70 页
【学位级别】：硕士
【文章目录】：
摘要
Abstract
Chapter 1 Introduction
1.1 Background and Significance
1.2 Literature Review
1.3 Thesis Outline
Chapter 2 A New Bivariate Binomial Model
2.1 Introduction of Model
2.2 Theoretical Properties
2.3 Estimation of Parameters
2.3.1 Maximum Likelihood Estimation
2.3.2 Bootstrap Confidence Interval
2.3.3 Parameter Estimation of Incomplete 2 × 2 Contingency Tables
2.4 Test of independence
2.4.1 Likelihood Ratio Test
2.4.2 Score Test
2.4.3 Wald test
2.4.4 Bootstrap Hypothesis Test
2.4.5 Bartlett-Corrected LRT
2.5 Brief Summary
Chapter 3 Multiple Comparison of Dependency Parameter
3.1 Multiple Comparison Problem
3.2 Controlling Methods for p-value
3.2.1 Bonferroni's Method
3.2.2 Sidak's Method
3.2.3 Holm's Method and Hochberg's Method
3.2.4 Hommel's Method
3.2.5 Benjamini-Hochberg Method and Benjamini-Yekutieli Method
3.3 Resampling Method
3.4 Brief Summary
Chapter 4 Simulation Studies
4.1 Accuracy of Point Estimators and Interval Estimators
4.2 Performance of Three Asymptotic Tests and the Bootstrap Test
4.3 A Real Data Example
4.4 Multiple Comparison
4.5 Brief Summary
Conclusions
结论
References
Appendix A First and Second Partial Derivatives of (2-23)
Appendix B Cumulants and their Derivatives for the Bartlett Correction Factor
Acknowledgements
本文编号：3274456
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