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Testing single-index restrictions with a focus on average derivatives

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  • Escanciano, Juan Carlos
  • Song, Kyungchul

Abstract

This paper considers a situation where the violation of a single-index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives. We propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives. The test has a limiting distribution under the null hypothesis, and even accommodates the case where the parameter estimates have a convergence rate slower than as in the case of maximum score estimation. The testing procedure can be easily modified when the main interest lies in average increment effects of binary covariates, multivariate average derivatives or linear restrictions other than those of average derivatives. Results from Monte Carlo experiments show that the asymptotic theory is a reasonable approximation of the finite-sample distributions and an application of our methods to female labor market participation illustrates the importance of this non-omnibus approach.

Suggested Citation

  • Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
  • Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:377-391
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    References listed on IDEAS

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    2. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    3. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    4. Xu, Kai & Zhou, Yeqing, 2021. "Projection-averaging-based cumulative covariance and its use in goodness-of-fit testing for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    5. Kyungchul Song, 2009. "Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling," PIER Working Paper Archive 09-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Kyungchul Song, 2009. "Two-Step Extremum Estimation with Estimated Single-Indices," PIER Working Paper Archive 09-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Kyungchul Song, 2009. "Bootstrapping Semiparametric Models with Single-Index Nuisance Parameters, Second Version," PIER Working Paper Archive 10-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 02 Aug 2010.
    8. Zhang, Yaowu & Zhou, Yeqing & Zhu, Liping, 2024. "A post-screening diagnostic study for ultrahigh dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).
    9. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    10. Ewa Strzalkowska-Kominiak & Ricardo Cao, 2014. "Beran-based approach for single-index models under censoring," Computational Statistics, Springer, vol. 29(5), pages 1243-1261, October.

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