Quantile Regression for Partially Linear Models with Missing Responses at Random

Abstract:

In this paper, we propose a weighted quantile regression method for partially linear models with missing response at random. The proposed estimation method can give an efficient estimator for parametric components, and can attenuate the effect of missing responses. Some simulations are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.

• Periodical: Applied Mechanics and Materials (Volumes 727-728)
• Pages: 1013-1016
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.727-728.1013
• Online since: January 2015
• Authors: Pei Xin Zhao*
• Keywords: Missing Data, Partially Linear Model, Quantile Regression

References

[1] R. Koenker and G.S. Bassett: Regression quantiles. Econometrica. Vol. 46 (1978), pp.33-50.

DOI: 10.2307/1913643

[2] W. Hendricks and R. Koenker: Hierarchical spline models for conditional quantiles and the demand for electricity. Journal of the American Statistical Association. Vol. 87 (1992), pp.58-68.

DOI: 10.1080/01621459.1992.10475175

[3] K. Yu and M.C. Jones: Local linear quantile regression. Journal of the American Statistical Association. Vol. 93 (1998), pp.228-237.

DOI: 10.1080/01621459.1998.10474104

[4] C.Y. Tang and C.L. Leng: An empirical likelihood approach to quantile regression with auxiliary information. Statistics & Probability Letters. Vol. 82 (2012), pp.29-36.

DOI: 10.1016/j.spl.2011.09.003

[5] S. Lee: Efficient semiparametric estimation of a partially linear quantile regression model. Econometric Theory. Vol. 19 (2003), pp.1-31.

DOI: 10.1017/s0266466603191013

[6] Y. Sun: Semiparametric efficient estimation of partially linear quantile regression models. The Annals of Economics and Finance. Vol. 6 (2005), pp.105-127.

[7] X. He and H. Liang: Quantile regression estimates for a class of linear and partially linear errors-in- variables models. Statistica Sinica. Vol. 10 (2000), pp.129-140.

[8] S. Chen and S. Khan: Semiparametric estimation of a partially linear censored regression model. Economic Theory. Vol. 17 (2001), p.567–590.

DOI: 10.1017/s0266466601173032

[9] H.J. Wang, Z. Zhu and J. Zhou: Quantile regression in partially linear varying coefficient models. The Annals of Statistics. Vol. 37 (2009), p.3841–3866.

DOI: 10.1214/09-aos695

[10] J.M. Robins, A. Rotnitzky and L. Zhao: Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association. Vol. 89 (1994), pp.846-866.

DOI: 10.1080/01621459.1994.10476818

[11] C.Y. Wang, S.J. Wang, L.P. Zhao and S.T. Ou, Weighted semiparametric estimation in regression analysis regression with missing covariates data. Journal of the American Statistical Association. Vol. 92 (1997), pp.512-525.

DOI: 10.1080/01621459.1997.10474004

[12] Q.H. Wang, O. Linton and W. Hardle: Semiparametric regression analysis with missing response at random. Journal of the American Statistical Association. Vol. 99 (2004), pp.334-345.

DOI: 10.1198/016214504000000449

[13] X. Lv and R. Li: Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables. Advances in Statistical Analysis. Vol. 97 (2013), pp.317-347.

DOI: 10.1007/s10182-013-0210-4

[14] L.G. Xue and D. Xue: Empirical likelihood for semiparametric regression model with missing response data. Journal of Multivariate Analysis. Vol. 102 (2011), pp.723-740.

DOI: 10.1016/j.jmva.2010.11.001

[15] R.J.A. Little and D.B. Rubin: Statistical Analysis with Missing Data, Wiley, New York (1987).