45
M-Test for Intercept After Pre-Testing
on Slope
Rossita M. Yunus
Shahjahan Khan
University of Southern Queensland
Australia
Email: yunus@usq.edu.au
khans@usq.edu.au
ABSTRACT
In the M-estimation methodology, a procedure was develop for
testing the intercept after pre-testing on the slope (Yunus and Khan,
in press). The (i) unrestricted test (UT), (ii) restricted test (RT) and
(iii) pre-test test (PTT) on intercept defined when the non-sample
prior information (NSPI) on the slope is (i) unknown, (ii) certain or
(iii) uncertain are considered. This paper investigates the
performance (size and power) of the UT, RT and PTT by introducing
the coefficient of variation. It is shown that the PTT achieves a
reasonable dominance over the other tests asymptotically and
performs better for larger coefficient of variation.
Keywords: pre-test, asymptotic size, asymptotic power, M-estimation,
regression model.
Introduction
A host of studies (Saleh, 2006, Khan and Saleh, 2001 and Khan et
al., 2002) found in literature were inspired by the idea of improving
the quality of inference in estimation by the inclusion of NSPI.
However, very little attention has been paid in improving the
performance of the test of the parameters.
Journal of Statistical Modeling and Analytics Vol. 1 No. 1, 45-57, 2010
ISSN 2180-3102
© 2010 Malaysia Institute of Statistics, Faculty of Computer and Mathematical Sciences,
Universiti Teknologi MARA (UiTM), Malaysia