An Approach to Nonparametric Regression in Moderate Dimensions

• Activity Number: 35
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mark Reimers*+
• Companies: Virginia Commonwealth University
• Keywords: nonparametric regression ; microarray normalization ; high dimensional data

Abstract

Several recent approaches to microarray normalization have attempted to estimate the biases on individual arrays as non-parametric functions of a moderate number (5-10) of technical variables describing the probes on the array. However these attempts have not employed a consistent methodology. Friedman's MARS fails in these problems, largely because the main effects are absent, by design of the array manufacturer.

The approach presented here is based on adapting radial basis functions (RBF) in a manner analogous to how MARS adapts linear regression. The key issue is how to spend degrees of freedom wisely, in order to achieve a flexible fit, with few overall degrees of freedom. The approach constructs ellipsoidal neighborhoods, in which the data set to be represented is modeled by a local linear function. The key is to efficiently find the directions of most departure from linearity.