Distance Tests Under Nonregular Conditions: Applications to the Comparative Calibration Model

Abstract

In this paper, we present a modification of the general distance test statistics under nonregular conditions with application to an special error-in-variables model. Specifically, we consider the comparative calibration model, a special case of the multivariate regression model. We compare, using artificial data, the power function of the distance test for restricted hypotheses with power functions of other general tests that were developed without the assumptions of errors in variables and restricted hypotheses occurring simultaneously. It is known that, when the Jacobian matrix of the restriction function describing the hypotheses has full rank, the asymptotic null distribution of the distance test statistic is a mixture of chi-square distributions. This assertion is not necessarily true when there are singular points in the null hypothesis. We suggest a modification to the distance test statistic which ensures convergence to a mixture of chi-square distributions. A real data set is analyzed according to the proposed methods.