Estimation and hypothesis testing in multivariate linear regression models under non normality


İSLAM M. Q.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.46, no.17, pp.8521-8543, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 17
  • Publication Date: 2017
  • Doi Number: 10.1080/03610926.2016.1183789
  • Title of Journal : COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Page Numbers: pp.8521-8543
  • Keywords: Least squares, maximum likelihood, modified maximum likelihood, multivariate linear regression, multivariate t-distribution, non normality, robustness, ESTIMATING PARAMETERS, NONNORMAL DISTRIBUTIONS, SYMMETRIC INNOVATIONS, AUTOREGRESSIVE MODELS, MAXIMUM-LIKELIHOOD, ROBUST ESTIMATION, SITUATIONS, SAMPLE

Abstract

This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariate t-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modified maximum likelihood estimation method that provides the estimator, called modified maximum likelihood estimator (MMLE), in closed form. These estimators are shown to be unbiased, efficient, and robust as compared to the widely used least square estimators (LSEs). Also, the tests based upon MMLEs are found to be more powerful than the similar tests based upon LSEs.