Comparative studies on the adequacy check of parametric measurement error models with auxiliary variable

Zhihua Sun, Dongshan Luo, Xiaohua Zhou and Qingzhao Zhang ()
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Zhihua Sun: University of Chinese Academy of Sciences
Dongshan Luo: Chinese Academy of Sciences
Xiaohua Zhou: Peking University
Qingzhao Zhang: Xiamen University

Statistical Papers, 2021, vol. 62, issue 4, No 7, 1723-1751

Abstract: Abstract The adequacy check of regression models is a fundamental approach to avoid model misspecifications. Three types of tests: the weighted integrated squared distance test, the U-statistic test and the empirical process based test, are very popular due to attractive theoretical merits such as consistency and satisfactory performances in practice. In this paper, we apply these three tests to check the adequacy of a mean parametric regression model with measurement error. By rigorously investigating the asymptotic properties of three testing methods under the null, local and global alternative hypotheses, we make detailed comparisons for the three tests. To the best of our knowledge, the results of these theoretical comparisons are novel. We conduct simulation studies and a real data analysis to compare the finite sample behaviors of the proposed methods.

Keywords: Weighted integrated squared distance test; U-statistic test; Empirical process based test; Power comparisons; Measurement error (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01154-3

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