Re-sampling Methods in Regression: Which Method to Use under Non-normality?

• Activity Number: 177
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Liliana Gonzalez*+ and Hend Auda
• Affiliation(s): University of Rhode Island and University of Rhode Island
• Keywords: Bootstrap ; Randomization ; Jackknife ; Testing Regression Coefficients ; Skewness ; Kurtosis

Abstract

Many different resampling methods have been developed to test the significance of a regression coefficient in multiple regression. These include the use of all different resampling methods: bootstrap, randomization, and jackknife. Some efforts to compare the performance of selected resampling methods in multiple regression have been made. These studies have compared the performance of methods when collinearity is present; errors are normally and exponentially distributed, and there are few outliers present.

Our main objective in this paper is to compare the performance of a more comprehensive list of re-sampling methods in regression used to test the significance of a coefficient in a multiple-regression model under departures from normality. In particular, we are interested in assessing the effect of skewness and kurtosis. The performance of the methods will be assessed via a simulation study by comparing their size and power, with errors simulated from several distributions and varying levels of skewness and kurtosis. We will also consider these approaches in relationship to real sets of environmental data and make recommendations concerning reliable approaches to data analysis.