The Robust Wald Test for Testing a Subset of Regression Parameters of a Multiple Regression Model with Apriori Information on Another Subset

Abstract

The classical and M-estimator-based robust Wald tests are introduced to simultaneously test an arbitrary
subset of coefficients of a multiple regression model when the remaining coefficients are either (i)
unspecified, (ii) specified with certainty or (iii) suspected with uncertainty. Under the three scenarios the
classical and robust Wald test statistics for (i) unrestricted (UT), (ii) restricted (RT) and (iii) pre-test (PTT)
tests are defined. The aims of the paper are to (i) define the classical and robust Wald UT, RT and PTT
statistics, (ii) find the asymptotic distribution of the test statistics (iii) determine the power function of the
tests and (iv) compare the performance of the robust Wald UT, RT and PTT to their classical counterparts
for large data. A Monte Carlo simulation study is conducted to obtainand compare the empirical power of
the tests. The simulation study shows a domination of the PTT over the UT and RT when the suspected
values are close to the true values and the robust Wald test is better than the its classical counterpart in terms
of size and power under a slight departure from normality assumption. An example with Olympic athlete
data is provided for illustration of the proposed method.