Browsing by Author "Tiku, ML"

Now showing 1 - 4 of 4

Citation - WoS: 59
Citation - Scopus: 62
Multiple linear regression model under nonnormality
(Taylor & Francis inc, 2004) Islam, MQ; Tiku, ML
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.
Citation - WoS: 27
Citation - Scopus: 29
Nonnormal regression. i. skew distributions
(Taylor & Francis inc, 2001) Islam, MQ; Tiku, ML; Yildirim, F
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.
Citation - WoS: 42
Citation - Scopus: 47
Nonnormal regression. II. Symmetric distributions
(Taylor & Francis inc, 2001) Tiku, ML; Islam, MQ; Selçuk, AS
Salient features of a family of short-tailed symmetric distributions, introduced recently by Tiku and Vaughan [1], 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 infers. 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] who develop modified likelihood methodology for skew distributions in the context of linear regression.
Citation - WoS: 19
Citation - Scopus: 21
Regression analysis with a dtochastic design variable
(Wiley, 2006) Sazak, HS; Tiku, ML; Islam, MQ
In 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.