Testing Multiple Inequality Hypotheses : A Smoothed Indicator Approach
Abstract
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby obviated. A simple procedure is enabled using fixed critical values. The test is shown to have correct asymptotic size in the uniform sense that supremum finite-sample rejection probability over null-restricted data distributions tends asymptotically to nominal significance level. This applies under weak assumptions allowing for estimator covariance singularity. The test is unbiased for a wide class of local alternatives. A new theorem establishes directions in which the test is locally most powerful. The proposed procedure is compared with predominant existing tests in structure, theory and simulation.
Cite
@article{arxiv.1206.6053,
title = {Testing Multiple Inequality Hypotheses : A Smoothed Indicator Approach},
author = {Le-Yu Chen and Jerzy Szroeter},
journal= {arXiv preprint arXiv:1206.6053},
year = {2012}
}