A block diagonal covariance matrix test and discriminant analysis of high-dimensional data
Publisher
Issued Date
2017
Issued Date (B.E.)
2560
Available Date
Copyright Date
Resource Type
Series
Edition
Language
eng
File Type
application/pdf
No. of Pages/File Size
155 leaves
ISBN
ISSN
eISSN
Other identifier(s)
b201075
Identifier(s)
Access Rights
Access Status
Rights
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Rights Holder(s)
Physical Location
National Institute of Development Administration. Library and Information Center
Bibliographic Citation
Citation
Poompong Kaewumpai (2017). A block diagonal covariance matrix test and discriminant analysis of high-dimensional data. Retrieved from: https://repository.nida.ac.th/handle/662723737/5784.
Title
A block diagonal covariance matrix test and discriminant analysis of high-dimensional data
Alternative Title(s)
Author(s)
Advisor(s)
Editor(s)
item.page.dc.contrubutor.advisor
Advisor's email
Contributor(s)
Contributor(s)
Abstract
In this dissertation, a new test statistic for testing for a block diagonal
covariance matrix structure with a multivariate normal population where the number
of variables
p
exceeds the number of observations
n
is proposed. Whereas classical
approaches such as the likelihood ratio test cannot be applied when
p n , the
proposed test statistic is based on the ratio of the estimators of
2
tr
and
2
trD
, where
is the population covariance matrix and
D
is the population covariance matrix
under the null hypothesis. Furthermore, the asymptotic distribution of the proposed
test statistic under the null hypothesis is standard normal. The performance of
proposed test statistic was assessed using a simulation study, in which empirical type I
error values and the empirical power were used to show its performance. The
empirical type I error values were close to the significance level and the empirical
power values were closed to 1 in all cases. Moreover, the performance of the proposed
test was compared with another previously reported test statistic, and the empirical
power values of the proposed test statistic were shown to be higher than those of the
comparative test statistic in some cases
Two new discriminant methods for high-dimensional data under the multivariate normal population with a block diagonal covariance matrix structure are also proposed. For the first method, the sample covariance matrix is approximated as a singular matrix based on the idea of reducing the dimensionality of the observations and using a well-conditioned covariance matrix. For the second method, a sample block diagonal covariance matrix is used instead. The performance of these two methods were compared with some of the previously reported methods via a simulation study, the results of which show that both proposed methods outperformed the other comparative methods under various conditions. In addition, the proposed test for testing block diagonal covariance matrix structure and the two new proposed methods for discriminant analysis were applied to a real-life dataset
Two new discriminant methods for high-dimensional data under the multivariate normal population with a block diagonal covariance matrix structure are also proposed. For the first method, the sample covariance matrix is approximated as a singular matrix based on the idea of reducing the dimensionality of the observations and using a well-conditioned covariance matrix. For the second method, a sample block diagonal covariance matrix is used instead. The performance of these two methods were compared with some of the previously reported methods via a simulation study, the results of which show that both proposed methods outperformed the other comparative methods under various conditions. In addition, the proposed test for testing block diagonal covariance matrix structure and the two new proposed methods for discriminant analysis were applied to a real-life dataset
Table of contents
Description
Thesis (Ph.D. (Statistics))--National Institute of Development Administration, 2017