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Nonnormal regression. I. Skew distributions
Date
2001-01-01
Author
İslam, Muhammed Qamarul
Yildirim, F
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Robustness
,
Maximum Likelihood;
,
Modified Maximum Likelihood
,
Least Squares
,
Weibull
,
Generalised Logistic
URI
https://hdl.handle.net/11511/48452
Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
DOI
https://doi.org/10.1081/sta-100104347
Collections
Department of Statistics, Article
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M. Q. İslam and F. Yildirim, “Nonnormal regression. I. Skew distributions,”
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
, pp. 993–1020, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48452.