Inference in multivariate linear regression models with elliptically distributed errors

Islam M. Q., Yildirim F., Yazici M.

JOURNAL OF APPLIED STATISTICS, cilt.41, sa.8, ss.1746-1766, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 8
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1080/02664763.2014.890177
  • Dergi Adı: JOURNAL OF APPLIED STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1746-1766
  • Anahtar Kelimeler: least-squares estimates, maximum likelihood estimates, modified maximum likelihood estimates, multivariate distributions, multivariate t-distribution, robust estimates, 62J05, 62F35, 62H12, MAXIMUM-LIKELIHOOD, PARAMETERS
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

In this study we investigate the problem of estimation and testing of hypotheses in multivariate linear regression models when the errors involved are assumed to be non-normally distributed. We consider the class of heavy-tailed distributions for this purpose. Although our method is applicable for any distribution in this class, we take the multivariate t-distribution for illustration. This distribution has applications in many fields of applied research such as Economics, Business, and Finance. For estimation purpose, we use the modified maximum likelihood method in order to get the so-called modified maximum likelihood estimates that are obtained in a closed form. We show that these estimates are substantially more efficient than least-square estimates. They are also found to be robust to reasonable deviations from the assumed distribution and also many data anomalies such as the presence of outliers in the sample, etc. We further provide test statistics for testing the relevant hypothesis regarding the regression coefficients.