1. Testing distribution for multiplicative distortion measurement errors.
- Author
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Cui, Leyi, Zhou, Yue, Zhang, Jun, and Yang, Yiping
- Subjects
- *
MONTE Carlo method , *MEASUREMENT errors , *RANDOM variables , *ASYMPTOTIC distribution , *PROBABILITY theory - Abstract
In this article, we study a goodness of fit test for a multiplicative distortion model under a uniformly distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. The proposed k-th power test statistic is based on logarithmic transformed observations and a correlation coefficient-based estimator without distortion measurement errors. The proper choice of k is discussed through the empirical coverage probabilities. The asymptotic null distribution of the test statistics are obtained with known asymptotic variances. Next, we proposed the conditional mean calibrated test statistic when a variable is distorted in a multiplicative fashion. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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