Electronic Journal of Statistics

Detecting column dependence when rows are correlated and estimating the strength of the row correlation

Omkar Muralidharan

Full-text: Open access

Abstract

Microarray experiments often yield a normal data matrix X whose rows correspond to genes and columns to samples. We commonly calculate test statistics Z=Xw, where Zi is a test statistic for the ith gene, and apply false discovery rate (FDR) controlling methods to find interesting genes. For example, Z could measure the difference in expression levels between treatment and control groups and we could seek differentially expressed genes. The empirical cdf of Z is important for FDR methods, since its mean and variance determine the bias and variance of FDR estimates. Efron (2009b) has shown that if the columns of X are independent, the variance of the empirical cdf of Z only depends on the mean-squared row correlation.

Microarray data, however, frequently shows signs of column dependence. In this paper, we show that Efron’s result still holds under column dependence, and give a conservative (upwardly biased) estimator for the mean-squared row correlation. We show Fisher’s transformation for sample correlations is still normalizing and variance stabilizing under column dependence, and use it to construct a permutation-invariant test of column independence. Finally, we argue that estimating the mean-squared row correlation under column dependence is impossible in general. Code to perform our test is available in the R package “colcor,” available on CRAN.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 1527-1546.

Dates
First available in Project Euclid: 23 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1293113417

Digital Object Identifier
doi:10.1214/10-EJS592

Mathematical Reviews number (MathSciNet)
MR2747132

Zentralblatt MATH identifier
1330.62307

Keywords
Fisher transformation sample correlation column dependence root mean squared correlation matrix normal

Citation

Muralidharan, Omkar. Detecting column dependence when rows are correlated and estimating the strength of the row correlation. Electron. J. Statist. 4 (2010), 1527--1546. doi:10.1214/10-EJS592. https://projecteuclid.org/euclid.ejs/1293113417


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