Multivariate Regression with Stable Errors Using Order Statistics

Abstract

In this paper, we investigate a multivariate regression model with multivariate heavy-tailed stable errors. Since in heavy-tailed data, especially in multivariate stable distributions, some moments do not exist; classical multivariate regression methods do not perform well. We suggest using an effective property of the existence of some moments of order statistics stable distribution. We propose a method for trimming the data set using this property. Then, we estimate the regression coefficients based on the rest of the ordered data. We calculate the trimmed data set based on the error’s tail index and skewness parameters. Also, we analytically compute the bias and variance of the introduced estimators of the regression parameters. Finally, we study the performance of the proposed methods with ordinary least squares via a simulation study and a real data set.