Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto

The microarray technology performs simultaneous analysis of thousands of genes in a massively parallel manner in one experiment, hence providing valuable knowledge on gene interaction and function. The understanding of microarray data has led to the development of new methods in statistics such...

Full description

Bibliographic Details
Main Author:	Karjanto, Suryaefiza
Format:	Book Section
Language:	English
Published:	Institute of Graduate Studies, UiTM 2017
Subjects:	Mathematical statistics. Probabilities Analysis
Online Access:	http://ir.uitm.edu.my/id/eprint/18970/ http://ir.uitm.edu.my/id/eprint/18970/1/ABS_SURYAEFIZA%20KARJANTO%20TDRA%20VOL%2012%20IGS%2017.pdf

id	uitm-18970
recordtype	eprints
spelling	uitm-189702018-06-07T01:56:12Z http://ir.uitm.edu.my/id/eprint/18970/ Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto Karjanto, Suryaefiza Mathematical statistics. Probabilities Analysis The microarray technology performs simultaneous analysis of thousands of genes in a massively parallel manner in one experiment, hence providing valuable knowledge on gene interaction and function. The understanding of microarray data has led to the development of new methods in statistics such as detection of differentially expressed genes. The microarray analysis was first employed for individual or single gene, but recently it has been applied to a gene set or a group of the gene. The relationship between genes in gene set is analysed using Hotelling’s T2 as a multivariate test statistic. However, the test cannot be applied when the number of samples is larger than the number of variables which is uncommon in the microarray. Since the microarray dataset typically consists of tens of thousands of genes from just dozens of samples due to various constraints, the sample covariance matrix is not positive definite and singular, thus it cannot be inverted. Thus, in this study, we proposed shrinkage approaches to estimating the covariance matrix in Hotelling’s T2 particularly to cater high dimensionality problem in microarray data. The Hotelling’s T2 statistic was combined with the shrinkage approach as an alternative estimation to estimate the covariance matrix in detect significant gene sets. The proposed shrinkage estimation approach is about taking a weighted average of the sample covariance matrix and a structured matrix or shrinkage target as shrinkage of the sample covariance matrix towards a target matrix of the same dimensions while the shrinkage intensity is the weight that the shrinkage target receives. Three shrinkage covariance methods were proposed in this study and are referred as ShrinkA, ShrinkB and ShrinkC.. Institute of Graduate Studies, UiTM 2017 Book Section PeerReviewed text en http://ir.uitm.edu.my/id/eprint/18970/1/ABS_SURYAEFIZA%20KARJANTO%20TDRA%20VOL%2012%20IGS%2017.pdf Karjanto, Suryaefiza (2017) Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto. In: The Doctoral Research Abstracts. IGS Biannual Publication, 12 (12). Institute of Graduate Studies, UiTM, Shah Alam.
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Teknologi MARA
building	UiTM Institutional Repository
collection	Online Access
language	English
topic	Mathematical statistics. Probabilities Analysis
spellingShingle	Mathematical statistics. Probabilities Analysis Karjanto, Suryaefiza Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto
description	The microarray technology performs simultaneous analysis of thousands of genes in a massively parallel manner in one experiment, hence providing valuable knowledge on gene interaction and function. The understanding of microarray data has led to the development of new methods in statistics such as detection of differentially expressed genes. The microarray analysis was first employed for individual or single gene, but recently it has been applied to a gene set or a group of the gene. The relationship between genes in gene set is analysed using Hotelling’s T2 as a multivariate test statistic. However, the test cannot be applied when the number of samples is larger than the number of variables which is uncommon in the microarray. Since the microarray dataset typically consists of tens of thousands of genes from just dozens of samples due to various constraints, the sample covariance matrix is not positive definite and singular, thus it cannot be inverted. Thus, in this study, we proposed shrinkage approaches to estimating the covariance matrix in Hotelling’s T2 particularly to cater high dimensionality problem in microarray data. The Hotelling’s T2 statistic was combined with the shrinkage approach as an alternative estimation to estimate the covariance matrix in detect significant gene sets. The proposed shrinkage estimation approach is about taking a weighted average of the sample covariance matrix and a structured matrix or shrinkage target as shrinkage of the sample covariance matrix towards a target matrix of the same dimensions while the shrinkage intensity is the weight that the shrinkage target receives. Three shrinkage covariance methods were proposed in this study and are referred as ShrinkA, ShrinkB and ShrinkC..
format	Book Section
author	Karjanto, Suryaefiza
author_facet	Karjanto, Suryaefiza
author_sort	Karjanto, Suryaefiza
title	Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto
title_short	Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto
title_full	Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto
title_fullStr	Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto
title_full_unstemmed	Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto
title_sort	shrinkage estimation of covariance matrix in hotelling’s t2 for differentially expressed gene sets / suryaefiza karjanto
publisher	Institute of Graduate Studies, UiTM
publishDate	2017
url	http://ir.uitm.edu.my/id/eprint/18970/ http://ir.uitm.edu.my/id/eprint/18970/1/ABS_SURYAEFIZA%20KARJANTO%20TDRA%20VOL%2012%20IGS%2017.pdf
first_indexed	2023-09-18T23:01:34Z
last_indexed	2023-09-18T23:01:34Z
_version_	1777418208544817152

Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto

Similar Items