COMPARATIVE ANALYSIS OF SHRINKAGE COVARIANCE MATRIX USING MICROARRAYS DATA

2016 ◽  
Vol 78 (4-4) ◽  
Author(s):  
Suryaefiza Karjanto ◽  
Norazan Mohamed Ramli ◽  
Nor Azura Md Ghani
Keyword(s):  
Covariance Matrix ◽  
Activity Level ◽  
Test Statistic ◽  
Multivariate Test ◽  
Hotelling's T2 ◽  
Gene Sets ◽  
Sample Covariance ◽  
Hotelling’S T2 ◽  
Hotelling’S T2 Statistic ◽  
Multivariate Test Statistic

The DNA microarray technologies permit scientists to depict the expression of genes for related samples.  This relationship between genes is analysed using Hotelling’s T2 as a multivariate test statistic but the disadvantage of this test, when used in microarray studies is the number of samples is larger than the number of variables.  This study discovers the potential of the shrinkage approach to estimate the covariance matrix specifically when the high dimensionality problem happened.  Consequently, the sample covariance matrix in Hotelling’s T2 statistic is not positive definite and become singular thus cannot be inverted.  In this research, the Hotelling’s T2 statistic is combined with a shrinkage approach as an alternative estimation to estimate the covariance matrix to detect significant gene sets.  The multivariate test statistic of classical Hotelling's T2 is used to integrate the correlation when assessing changes in activity level across biological conditions.  The performances of the proposed methods were assessed using real data study.  Shrinkage covariance matrix approach indicates a better result for detection of differentially expressed gene sets as compared to other methods.

Linear Combination Test for Hierarchical Gene Set Analysis

2011 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiaoming Wang ◽  
Irina Dinu ◽  
Wei Liu ◽  
Yutaka Yasui
Keyword(s):  
Gene Expression ◽  
Linear Combination ◽  
Covariance Matrix ◽  
Gene Set Analysis ◽  
Gene Set ◽  
Hotelling's T2 ◽  
Gene Sets ◽  
Hotelling’S T2 ◽  
Combination Test ◽  
Linear Combination Test

Gene-set analysis (GSA) aims to identify sets of differentially expressed genes by a phenotype in DNA microarray studies. Challenges occur due to the salient characteristics of the data: (1) the number of genes is far larger than the number of observations; (2) gene expression measurements, especially within each gene set, can be highly correlated; and (3) the number of gene sets that can be examined is large and increasing rapidly. These challenges call for gene-set testing procedures that have both efficiency in computation for large GSAs and high power in the presence of the high correlation.We propose a new GSA approach called Linear Combination Test (LCT), incorporating the covariance matrix estimator of gene expression into the test statistic. The proposed LCT and two other GSA methods, a mod-ification of Hotelling’s T2 using a shrinkage covariance matrix and our SAM-GS (Dinu et. al. 2007), the two methods that have been reported by Tsai and Chen (2009) to perform best in terms of power, are evaluated in simulation studies and a real microarray study. The LCT method is more computationally efficient than the modified Hotelling’s T2 and approximates the superb power of the modified Hotelling’s T2. LCT is slightly faster than SAM-GS, but more powerful, due to incorporating the covariance matrix estimator. An extra step to enhance the interpretation of GSA results is also proposed in the form of a hierarchical LC (HLC) testing procedure, providing scientists useful hierarchical information on gene sets that LCT identified as differentially expressed.Availability: A free R-code to perform LCT-GSA and HLC test is available at http://www.ualberta.ca/~yyasui/homepage.html.

scholarly journals Robust Hotelling’s T2 statistic based on M-estimator

2021 ◽  
Vol 1988 (1) ◽  
pp. 012116
Author(s):  
Mohd Aizat Ahlam Mohamad Mokhtar ◽  
Nur Syahidah Yusoff ◽  
Chuan Zun Liang
Keyword(s):  
Hotelling's T2 ◽  
M Estimator ◽  
Hotelling’S T2 ◽  
Hotelling’S T2 Statistic

scholarly journals How to keep the Type I Error Rate in ANOVA if Variances are Heteroscedastic

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Karl Moder
Keyword(s):  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Underlying Distribution ◽  
Hotelling's T2 ◽  
Type I Error Rate ◽  
Hotelling’S T2 ◽  
F Distribution ◽  
Alternative Test

One essential prerequisite to ANOVA is homogeneity of variances in underlying populations. Violating this assumption may lead to an increased type I error rate. The reason for this undesirable effect is due to the calculation of the corresponding F-value. A slightly different test statistic keeps the level ®. The underlying distribution of this alternative method is Hotelling’s T2. As Hotelling’s T2 can be approximated by a Fisher’s F-distribution, this alternative test is very similar to an ordinary analysis of variance.

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