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Specification tests for regression models with measurement errors

Xiaojun Song, Jichao Yuan

arXiv 6 Nov 2025 · Econometrics

arXiv:2511.04127 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In this paper, we propose new specification tests for regression models with measurement errors in the explanatory variables. Inspired by the integrated conditional moment (ICM) approach, we use a deconvoluted residual-marked empirical process and construct ICM-type test statistics based on it. The issue of measurement errors is addressed by applying a deconvolution kernel estimator in constructing the residuals. We demonstrate that employing an orthogonal projection onto the tangent space of nuisance parameters not only eliminates the parameter estimation effect but also facilitates the simulation of critical values via a computationally simple multiplier bootstrap procedure. It is the first time a multiplier bootstrap has been proposed in the literature of specification testing with measurement errors. We also develop specification tests and the multiplier bootstrap procedure when the measurement error distribution is unknown. The finite-sample performance of the proposed tests for both known and unknown measurement error distributions is evaluated through Monte Carlo simulations, which demonstrate their efficacy.

Citation extraction

42
references
89
in-text mentions
42
distinct cited
3
self-citations
12,418
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Otsu, T. and Taylor, L (2021) Specification testing for errors-in-variables models1.000126100%
2Meister, A (2009) Deconvolution problems in nonparametric statistics1.00054100%
3Dong, H. and Taylor, L (2022) Nonparametric significance testing in measurement error models0.8749567%
4Delaigle, A., Hall, P., and Meister, A (2008) On deconvolution with repeated measurements0.81142100%
5Bierens, H. J (1982) Consistent model specification tests0.73732100%
6Hall, P. and Ma, Y (2007) Testing the suitability of polynomial models in errors-in-variables problems0.73732100%
7Sant’Anna, P. H. and Song, X (2019) Specification tests for the propensity score self0.73732100%
8van der Vaart, A. W. and Wellner, J. A (1996) Weak Convergence and Empirical Processes0.73732100%
9Bierens, H. J. and Ploberger, W (1997) Asymptotic theory of integrated conditional moment tests0.64422100%
10Taupin, M.-L (1998) Estimation in the nonlinear errors-in-variables model0.64422100%

Showing the top 10 of 42 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Testing Heteroskedasticity Under Measurement Error0.00021