Selecting Local Models in Multiple Regression by Maximizing Power

2006/12/10 by Chad Schafer, Chad M. Schafer, Schafer, Chad M. +2
Computer Science · Mathematics · #62G08 #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G08 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0612248

30 pages, 14 postscript figures

arxiv created 2006/12/10 · openalex publication_date 2006/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers multiple regression procedures for analyzing the relationship between a response variable and a vector of covariates in a nonparametric setting where both tuning parameters and the number of covariates need to be selected. We introduce an approach which handles the dilemma that with high dimensional data the sparsity of data in regions of the sample space makes estimation of nonparametric curves and surfaces virtually impossible. This is accomplished by abandoning the goal of trying to estimate true underlying curves and instead estimating measures of dependence that can determine important relationships between variables.

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