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Nonnormal Regression.I. Skew Distributions
(2001) Islam, M. Qamarul; L. Tiku, Moti; Yildirim, F.
In a linear regression model of the typey¼ Xþe, it is oftenassumed that the random erroreis normally distributed. Innumerous situations, e.g., whenymeasures life times or reac-tion times,etypically has a skew distribution. We considertwo important families of skew distributions, (a) Weibull withsupport IR:ð0,1Þon the real line, and (b) generalised logisticwit hsupport IR:ð 1,1Þ. Since the maximum likelihoodestimators are intractable in these situations, we derivemodified likelihood estimators which have explicit algebraicforms and are, therefore, easy to compute. We show that theseestimators are remarkably efficient, and robust. We develophypothesis testing procedures and give a real life example
Citation - WoS: 4
Citation - Scopus: 4
Estimation in Multivariate Nonnormal Distributions With Stochastic Variance Function
(Elsevier Science Bv, 2014) Islam, M. Qamarul; Qamarul Islam, M.
In this paper the problem of estimation of location and scatter of multivariate nonnormal distributions is considered. Estimators are derived under a maximum likelihood setup by expressing the non-linear likelihood equations in the linear form. The resulting estimators are analytical expressions in terms of sample values and, hence, are easily computable and can also be manipulated analytically. These estimators are found to be remarkably more efficient and robust as compared to the least square estimators. They also provide more powerful tests in testing various relevant statistical hypotheses. (C) 2013 Elsevier B.V. All rights reserved.

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