title: Conditional Density Estimation in Measurement Error Problems.
abstract: This paper is motivated by a wide range of background correction problems in gene array data analysis, where the raw gene expression intensities are measured with error. Estimating a conditional density function from the contaminated expression data is a key aspect of statistical inference and visualization in these studies. We propose re-weighted deconvolution kernel methods to estimate the conditional density function in an additive error model, when the error distribution is known as well as when it is unknown. Theoretical properties of the proposed estimators are investigated with respect to the mean absolute error from a "double asymptotic" view. Practical rules are developed for the selection of smoothing-parameters. Simulated examples and an application to an Illumina bead microarray study are presented to illustrate the viability of the methods.
authors.affiliation: Department of Quantitative Health Sciences / Biostatistics Section, Cleveland Clinic Lerner Research Institute, Cleveland, OH 44195, USA.
authors.forename: Xiao-Feng
authors.initials: XF
authors.lastname: Wang
authors.affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada.
authors.forename: Deping
authors.initials: D
authors.lastname: Ye
keywords: bandwidth selection; conditional density; deconvolution; gene microarray; kernel; measurement error; ridge parameter