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Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/402
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Article Multiple linear regression model under nonnormality(Taylor & Francis Inc, 2004) Islam, M. Qamarul; Tiku, Moti L.We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.Article 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 exampleArticle Citation - WoS: 4Citation - Scopus: 4Estimation 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.Article Citation - WoS: 4Citation - Scopus: 6Mahalanobis Distance Under Non-Normality(Taylor & Francis Ltd, 2010) Tiku, Moti L.; Islam, M. Qamarul; Qumsiyeh, Sahar B.We give a novel estimator of Mahalanobis distance D2 between two non-normal populations. We show that it is enormously more efficient and robust than the traditional estimator based on least squares estimators. We give a test statistic for testing that D2=0 and study its power and robustness properties.Article Citation - WoS: 13Citation - Scopus: 13Multiple Linear Regression Model With Stochastic Design Variables(Taylor & Francis Ltd, 2010) Islam, M. Qamarul; Tiku, Moti L.In a simple multiple linear regression model, the design variables have traditionally been assumed to be non-stochastic. In numerous real-life situations, however, they are stochastic and non-normal. Estimators of parameters applicable to such situations are developed. It is shown that these estimators are efficient and robust. A real-life example is given.