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Testing Heteroskedasticity Under Measurement Error

Xiaojun Song, Jichao Yuan

arXiv 19 May 2026 · Econometrics

arXiv:2605.20012 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test statistics based on a deconvolved residual-marked empirical process and establish their asymptotic properties in both ordinary smooth and supersmooth cases, assuming the measurement error distribution is known. The issue of an unknown measurement error distribution is addressed by employing estimators of the measurement error characteristic function based on repeated measurements. Furthermore, depending on whether the measurement error distribution is known or not, to obtain critical values from the case-dependent limiting null distributions, we propose two computationally attractive multiplier bootstrap methods where the "parameter estimation effect" is successfully addressed. Finally, simulation results and empirical studies about corn yields and household budget shares confirm the favorable properties of the proposed tests.

Citation extraction

57
references
100
in-text mentions
57
distinct cited
4
self-citations
13,646
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
1Dong, H. and Taylor, L (2022) Nonparametric significance testing in measurement error models0.93511782%
2Delaigle, A., Hall, P., and Meister, A (2008) On deconvolution with repeated measurements0.92844100%
3van der Vaart, A. W. and Wellner, J. A (1996) Weak Convergence and Empirical Processes0.8746367%
4Durbin, J (1973) Distribution theory for tests based on the sample distribution function0.84333100%
5Carroll, R. J. and Spiegelman, C. H (1992) Diagnostics for nonlinearity and heteroscedasticity in errors-in-variables regression0.73732100%
6Fuller, W. A (2009) Measurement error models0.64441100%
7Hausman, J. A., Newey, W. K., and Powell, J. L (1995) Nonlinear errors in variables estimation of some engel curves0.64441100%
8Bierens, H. J (1982) Consistent model specification tests0.64422100%
9Bierens, H. J (1990) A consistent conditional moment test of functional form0.64422100%
10Carroll, R. J. and Hall, P (1988) Optimal rates of convergence for deconvolving a density0.64422100%

Showing the top 10 of 57 scored citations.