Xiaojun Song, Jichao Yuan
arXiv 6 Nov 2025 · Econometrics
arXiv:2511.04127 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Otsu, T. and Taylor, L (2021) Specification testing for errors-in-variables models | 1.000 | 12 | 6 | 100% |
| 2 | Meister, A (2009) Deconvolution problems in nonparametric statistics | 1.000 | 5 | 4 | 100% |
| 3 | Dong, H. and Taylor, L (2022) Nonparametric significance testing in measurement error models | 0.874 | 9 | 5 | 67% |
| 4 | Delaigle, A., Hall, P., and Meister, A (2008) On deconvolution with repeated measurements | 0.811 | 4 | 2 | 100% |
| 5 | Bierens, H. J (1982) Consistent model specification tests | 0.737 | 3 | 2 | 100% |
| 6 | Hall, P. and Ma, Y (2007) Testing the suitability of polynomial models in errors-in-variables problems | 0.737 | 3 | 2 | 100% |
| 7 | Sant’Anna, P. H. and Song, X (2019) Specification tests for the propensity score self | 0.737 | 3 | 2 | 100% |
| 8 | van der Vaart, A. W. and Wellner, J. A (1996) Weak Convergence and Empirical Processes | 0.737 | 3 | 2 | 100% |
| 9 | Bierens, H. J. and Ploberger, W (1997) Asymptotic theory of integrated conditional moment tests | 0.644 | 2 | 2 | 100% |
| 10 | Taupin, M.-L (1998) Estimation in the nonlinear errors-in-variables model | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 42 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Testing Heteroskedasticity Under Measurement Error | 0.000 | 2 | 1 |