| Abstract: | Salient features of a family of short-tailed symmetric distributions, introduced recently by Tiku and Vaughan 1] Tiku, M. L. and Vaughan, D. C. 1999. “A family of short-tailed symmetric distributions”. In Technical Report Canada: McMaster University. Google Scholar], are enunciated. Assuming the error distribution to be one of this family, the methodology of modified likelihood is used to derive MML estimators of parameters in a linear regression model. The estimators are shown to be efficient, and robust to inliers. This paper is essentially the first to achieve robustness to inliers. The methodology is extended to long-tailed symmetric distributions and the resulting estimators are shown to be efficient, and robust to outliers. This paper should be read in conjunction with Islam et al. 2] Islam, Q., Tiku, M. L. and Yildirim, F. 2001. Nonnormal regression, Part I: Skew distributions. Commun. Stat.—Theory Meth., to appear Google Scholar]who develop modified likelihood methodology for skew distributions in the context of linear regression. |
