Type
Text
Type
Dissertation
Advisor
Finch, Stephen J.Zhu, Wei | Mendell, Nancy R. | Lo, Yungtai.
Date
2011-12-01
Keywords
bivariate, bootstrap, LRT, mixture, power | Statistics
Department
Department of Applied Mathematics and Statistics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71257
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Univariate analysis has been commonly used in the studies of disease-related phenotypes. The need for multivariate analysis on linkage studies of complex disease/traits has grown with the increasing use of multiple phenotypes. This research extends the model for testing a single bivariate normal distribution versus a two component bivariate normal mixture distribution. Previous research restricted the two variables to have equal means and variance. Our study considers the more general case with no restrictions on these parameter values. Simulations are used to conduct a power study of bootstrap test under different combinations of parameter values. We note that samples of sample size n = 200 or more and an average mixture effect size of 2.5 or more is needed with mixing proportions between 0.1 and 0.9 to achieve reasonable power. Regression models of LRT statistic values are also fitted to calculate the type I error rate and power. Finally the bootstrap method is shown to be a reliable approach for evaluating the LRT statistics. | 88 pages
Recommended Citation
He, Tingting, "The Bivariate Normal Mixture Distribution: A Power Study of Bootstrap Test" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 463.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/463