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Minimum distance model checking in Berkson measurement error models with validation data

Author

Listed:
  • Pei Geng

    (Illinois State University)

  • Hira L. Koul

    (Michigan State University)

Abstract

This article studies a minimum distance regression model checking approach in the presence of Berkson measurement errors in covariates without specifying the measurement error density but when external validation data are available. The proposed tests are based on a class of minimized integrated square distances between a nonparametric estimate of the calibrated regression function and the parametric null model being fitted. The asymptotic distributions of these tests under the null hypothesis and against certain alternatives are established. Surprisingly, these asymptotic distributions are the same as in the case of known measurement error density. In comparison, the asymptotic distributions of the corresponding minimum distance estimators of the null model parameters are affected by the estimation of the calibrated regression function. A simulation study shows desirable performance of a member of the proposed class of estimators and tests.

Suggested Citation

  • Pei Geng & Hira L. Koul, 2019. "Minimum distance model checking in Berkson measurement error models with validation data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 879-899, September.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:3:d:10.1007_s11749-018-0610-6
    DOI: 10.1007/s11749-018-0610-6
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    References listed on IDEAS

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    1. Susanne M. Schennach, 2013. "Regressions with Berkson errors in covariates - A nonparametric approach," Papers 1308.2836, arXiv.org.
    2. Grace Y. Yi & Yanyuan Ma & Donna Spiegelman & Raymond J. Carroll, 2015. "Functional and Structural Methods With Mixed Measurement Error and Misclassification in Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 681-696, June.
    3. Hardle, W. & Marron, J.S. & Wand, Mp., 1990. "Bandwith choice for density derivatives," LIDAM Reprints CORE 945, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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