Parametric hypothesis tests for exponentiality under multiplicative distortion measurement errors data

In this paper, we proposed a parametric hypothesis test of the multiplicative distortion model under the exponentially distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. Firstly, some new test statistics are proposed to checking the exponential distribution assumption without distortion effects. Next, we proposed several test statistics when the variable is distorted in the multiplicative fashion. For the latter, the proposed test statistics automatically eliminate the distortion effects involved in the unobserved variable. The proposed test statistics with or without distortions are all asymptotical free, and the asymptotic null distribution of the test statistics are obtained with known asymptotic variances. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. These methods are applied to analyze four real datasets for illustrations.