PARAMETRIC AND NON-PARAMETRIC BOOTSTRAP: A SIMULATION STUDY FOR A LINEAR REGRESSION WITH RESIDUALS FROM A MIXTURE OF LAPLACE DISTRIBUTIONS

Abstract

In this simulation study, we compared ordinary least squares (OLS), weighted least squares (WLS), and three bootstrap versions (resampling of data points, resampling residuals, generating new residuals from Laplace distributions) for a linear regression with independent residuals from a mixture of two Laplace distributions. Leverage points were removed from the data, more outliers were added, and knowledge about the two Laplace distributions was omitted. For the data set with more extreme outliers, all methods showed problems with the coverage probability of the confidence intervals for parameter estimation, but bootstrap method 1 was clearly more robust. For the base data set, there was no difference between bootstrap and WLS, similarly to the data set with some leverage points removed. Without knowledge of the two Laplace distributions, bootstrap method 2 performed best in that standard errors of the parameter estimates was lower and confidence intervals shorter. This result suggests that, depending on the sample kurtosis compared to distribution kurtosis, bootstrap method 2 (non-parametric) or 3 (parametric) is better.