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


İSLAM M. Q.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.46, ss.8521-8543, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 46 Konu: 17
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/03610926.2016.1183789
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Sayfa Sayıları: ss.8521-8543

Özet

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.