Testing distribution for multiplicative distortion measurement errors

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...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2025-03, Vol.54 (5), p.1545-1567
Main Authors: Cui, Leyi, Zhou, Yue, Zhang, Jun, Yang, Yiping
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Calibration
Correlation coefficients
Distortion
Errors
Goodness of fit
kernel smoothing
Monte Carlo simulation
multiplicative distortions
Random variables
Statistical tests
Citations: Items that this one cites
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2024.2347330