The Annals of Statistics

Nonparametric estimation of genewise variance for microarray data

Jianqing Fan, Yang Feng, and Yue S. Niu

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Abstract

Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman–Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the sample size and it is not obvious how the variance function can be estimated when measurements are correlated. In such a high-dimensional nonparametric problem, we proposed two novel nonparametric estimators for genewise variance function and semiparametric estimators for measurement correlation, via solving a system of nonlinear equations. Their asymptotic normality is established. The finite sample property is demonstrated by simulation studies. The estimators also improve the power of the tests for detecting statistically differentially expressed genes. The methodology is illustrated by the data from microarray quality control (MAQC) project.

Article information

Source
Ann. Statist. Volume 38, Number 5 (2010), 2723-2750.

Dates
First available in Project Euclid: 11 July 2010

Permanent link to this document
http://projecteuclid.org/euclid.aos/1278861458

Digital Object Identifier
doi:10.1214/10-AOS802

Mathematical Reviews number (MathSciNet)
MR2722454

Zentralblatt MATH identifier
1200.62133

Subjects
Primary: 62G05: Estimation
Secondary: 62P10: Applications to biology and medical sciences

Keywords
Genewise variance estimation gene selection local linear regression nonparametric model correlation correction validation test

Citation

Fan, Jianqing; Feng, Yang; Niu, Yue S. Nonparametric estimation of genewise variance for microarray data. Ann. Statist. 38 (2010), no. 5, 2723--2750. doi:10.1214/10-AOS802. http://projecteuclid.org/euclid.aos/1278861458.


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