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Simultaneous Inference Procedures in the Presence of Heteroscedasticity

li, meng
http://rave.ohiolink.edu/etdc/view?acc_num=osu1503002070774959

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Statistics.
Simultaneous inference has become an increasingly important statistical tool in handling many real world problems. In a frequentist analysis, performing simultane- ous inference typically requires exploring the null distribution of the multivariate test statistic in order to control the resulting inference at the pre-determined nominal level. As the probability calculation of the true null distribution involves high-dimensional integration that was computationally too dicult before the prevalence of computing resources, simultaneous inferences were only available for some special designs with speci c sample size patterns in the one-way analysis of variance setting. With the dramatic rise in computing power, numerical calculation of the multivari- ate t probability becomes accessible, enabling one to perform simultaneous analyses in the general linear model framework assuming homogeneous variance. In this case, the null distribution of the test statistic for any set of linear hypotheses is a multivariate t distribution. In this dissertation, we devise a computationally ecient algorithm to calculate the tail areas and nd the critical values of any arbitrary multivariate t distribution. The performance of the algorithm is compared to the existing method with regard to the accuracy of inference and computing time. In particular, the re- striction on integer degrees of freedom of the current practice is relaxed in the new algorithm. An additional bene t of the new algorithm is the allowance for the error probability for each individual comparison to vary. However, in the presence of heteroscedasticity, the true null distribution is un- known and often replaced by a computationally tractable approximation that is in- stead used for inference. The performance of the resulting inferential procedures is impacted by the discrepancy between the true null distribution and its approximation. Suggested by the lack of control over the family-wise error rate caused by failing to account for the dependence structure among the denominators of the test statistic of the Plug-in procedure { a common approach for multiple inference in the presence of heteroscedasticity { this dissertation develops an inferential procedure that exploits the dependence structure of the components of the test statistic more precisely. The suggested approach approximates the unknown true null distribution by a variation of the classical multivariate t distribution, referred to as the generalized multivariate t distribution. We propose an extension of the numerical algorithm for the classical multivariate t probability calculation to accommodate the general- ized multivariate t. In addition to the accuracy gained by incorporating the depen- dence structure among the denominators into the procedure compared to the Plug-in method, the computing time is considerably reduced. With the remarkable developments in statistical models, it becomes increasingly important to consider the impact that modeling choices have on the subsequent para- metric inferences. We investigate the e ect of modeling strategies on the inference in a special setting where the data generating process is a blend of two qualitatively separate portions { one portion is stable and amenable to modeling while another portion is unstable. Together, the reliability of the resulting inference on the truth can be attributable to multiple sources including, but not limited to, the model as a description of the mechanism and the inference procedure as assessed in this work.
Steven MacEachern (Advisor)
171 p.
Statistics
Heteroscedasticity, Multiple Comparisons, NORTA, Multiplicity-adjusted critical values, spherical radial transformation, multivariate quantile

Recommended Citations

Citations

  • li, M. (2017). Simultaneous Inference Procedures in the Presence of Heteroscedasticity [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503002070774959

    APA Style (7th edition)

  • li, meng. Simultaneous Inference Procedures in the Presence of Heteroscedasticity. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1503002070774959.

    MLA Style (8th edition)

  • li, meng. "Simultaneous Inference Procedures in the Presence of Heteroscedasticity." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503002070774959

    Chicago Manual of Style (17th edition)

osu1503002070774959
271
© 2017, some rights reserved.Creative Commons License Simultaneous Inference Procedures in the Presence of Heteroscedasticity by meng li is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.