Nonnormal regression. I. Skew distributions

Islam M., Tiku M., Yildirim F.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.30, sa.6, ss.993-1020, 2001 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 6
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1081/sta-100104347
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.993-1020
  • Anahtar Kelimeler: robustness, maximum likelihood, modified maximum likelihood, least squares, Weibull, generalised logistic, MAXIMUM-LIKELIHOOD, PARAMETERS
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

In a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we derive modified likelihood estimators which have explicit algebraic forms and are, therefore, easy to compute. We show that these estimators are remarkably efficient, and robust. We develop hypothesis testing procedures and give a real life example.