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Biometrika 2008 95(2):437-449; doi:10.1093/biomet/asn017
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© 2008 Biometrika Trust

Articles

Nonparametric variance estimation in the analysis of microarray data: a measurement error approach

Raymond J. Carroll

Department of Statistics, Texas A&M University, College Station, Texas 77843-3143, U.S.A. carroll{at}stat.tamu.edu

Yuedong Wang

Department of Statistics, and Applied Probability, University of California, Santa Barbara, California 93106, U.S.A. yuedong{at}pstat.ucsb.edu

Received for publication 1 March 2007. Revision received 1 December 2007.
  Abstract

We investigate the effects of measurement error on the estimation of nonparametric variance functions. We show that either ignoring measurement error or direct application of the simulation extrapolation, SIMEX, method leads to inconsistent estimators. Nevertheless, the direct SIMEX method can reduce bias relative to a naive estimator. We further propose a permutation SIMEX method that leads to consistent estimators in theory. The performance of both the SIMEX methods depends on approximations to the exact extrapolants. Simulations show that both the SIMEX methods perform better than ignoring measurement error. The methodology is illustrated using microarray data from colon cancer patients.

Key Words: Heteroscedasticity • Local polynomial regression • Measurement error • Microarray • Nonparametric regression • Permutation • SIMEX • Simulation-extrapolation • Variance function estimation


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