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Partially linear varying coefficient models with missing at random responses

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  • Francesco Bravo

Abstract

This paper considers partially linear varying coefficient models when the response variable is missing at random. The paper uses imputation techniques to develop an omnibus specification test. The test is based on a simple modification of a Cramer von Mises functional that overcomes the curse of dimensionality often associated with the standard Cramer von Mises functional. The paper also considers estimation of the mean functional under the missing at random assumption. The proposed estimator lies in between a fully nonparametric and a parametric one and can be used, for example, to obtain a novel estimator for the average treatment effect parameter. Monte Carlo simulations show that the proposed estimator and test statistic have good finite sample properties. An empirical application illustrates the applicability of the results of the paper. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Francesco Bravo, 2013. "Partially linear varying coefficient models with missing at random responses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 721-762, August.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:721-762
    DOI: 10.1007/s10463-012-0391-8
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    1. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    2. Brian R. Copeland & M. Scott Taylor, 2004. "Trade, Growth, and the Environment," Journal of Economic Literature, American Economic Association, vol. 42(1), pages 7-71, March.
    3. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    4. Sun, Zhihua & Wang, Qihua & Dai, Pengjie, 2009. "Model checking for partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 636-651, April.
    5. Francesco Bravo & David Jacho-Chavez, 2011. "Empirical Likelihood for Efficient Semiparametric Average Treatment Effects," Econometric Reviews, Taylor & Francis Journals, vol. 30(1), pages 1-24.
    6. repec:adr:anecst:y:2006:i:81:p:02 is not listed on IDEAS
    7. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    8. Francesco Bravo, 2012. "Generalized empirical likelihood testing in semiparametric conditional moment restrictions models," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-31, February.
    9. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    10. Miguel A. Delgado & Manuel A. Dominguez & Pascal Lavergne, 2006. "Consistent Tests of Conditional Moment Restrictions," Annals of Economics and Statistics, GENES, issue 81, pages 33-67.
    11. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    12. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    13. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    14. Jeffrey A. Frankel & Andrew K. Rose, 2005. "Is Trade Good or Bad for the Environment? Sorting Out the Causality," The Review of Economics and Statistics, MIT Press, vol. 87(1), pages 85-91, February.
    15. Millimet, Daniel L. & Tchernis, Rusty, 2009. "On the Specification of Propensity Scores, With Applications to the Analysis of Trade Policies," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 397-415.
    16. Whang, Yoon-Jae, 2001. "Consistent specification testing for conditional moment restrictions," Economics Letters, Elsevier, vol. 71(3), pages 299-306, June.
    17. Fan, Jianqing & Wu, Yichao, 2008. "Semiparametric Estimation of Covariance Matrixes for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1520-1533.
    18. Winfried Stute & Li‐Xing Zhu, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545, September.
    19. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    20. Liqun Wang & Alexandre Leblanc, 2008. "Second-order nonlinear least squares estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 883-900, December.
    21. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    22. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    23. Mijeong Kim & Yanyuan Ma, 2012. "The efficiency of the second-order nonlinear least squares estimator and its extension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 751-764, August.
    24. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
    25. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    26. repec:hal:journl:peer-00732534 is not listed on IDEAS
    27. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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    Cited by:

    1. Jun Zhang & Nanguang Zhou & Zipeng Sun & Gaorong Li & Zhenghong Wei, 2016. "Statistical inference on restricted partial linear regression models with partial distortion measurement errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 304-331, November.

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