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Goodness-of-fit tests in linear EV regression with replications

Author

Listed:
  • Weijia Jia

    (Kansas State University)

  • Weixing Song

    (Kansas State University)

Abstract

This paper proposes a goodness-of-fit test for checking the adequacy of parametric forms of the regression error density functions in linear errors-in-variables regression models. Instead of assuming the distribution of the measurement error to be known, we assume that replications of the surrogates of the latent variables are available. The test statistic is based upon a weighted integrated squared distance between a nonparametric estimator and a semi-parametric estimator of the density functions of certain residuals. Under the null hypothesis, the test statistic is shown to be asymptotically normal. Consistency and local power results of the proposed test under fixed alternatives and local alternatives are also established. Finite sample performance of the proposed test is evaluated via simulation studies. A real data example is also included to demonstrate an application of the proposed test.

Suggested Citation

  • Weijia Jia & Weixing Song, 2018. "Goodness-of-fit tests in linear EV regression with replications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 395-421, May.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:4:d:10.1007_s00184-018-0648-1
    DOI: 10.1007/s00184-018-0648-1
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    References listed on IDEAS

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    4. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
    5. Giménez, Patricia & Patat, María Laura, 2005. "Estimation in comparative calibration models with replicate measurement," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 155-164, February.
    6. Holzmann, Hajo & Bissantz, Nicolai & Munk, Axel, 2007. "Density testing in a contaminated sample," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 57-75, January.
    7. Huwang, L., 1995. "Interval Estimation in Structural Errors-in-Variables Model with Partial Replication," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 230-245, November.
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