WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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 Citation - WoS: 62Citation - Scopus: 64Multiple Linear Regression Model Under Nonnormality(Taylor & Francis inc, 2004) Islam, MQ; Tiku, MLWe 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 Citation - WoS: 27Citation - Scopus: 29Nonnormal Regression. I. Skew Distributions(Taylor & Francis inc, 2001) Islam, MQ; Tiku, ML; Yildirim, FIn 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.Article 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.Article Citation - WoS: 20Citation - Scopus: 22Regression Analysis With a Dtochastic Design Variable(Wiley, 2006) Sazak, HS; Tiku, ML; Islam, MQIn regression models, the design variable has primarily been treated as a nonstochastic variable. In numerous situations, however, the design variable is stochastic. The estimation and hypothesis testing problems in such situations are considered. Real life examples are given.