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Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables

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  • Xiaofeng Lv

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  • Rui Li

    ()

Abstract

In this paper, we consider the estimation and inference of the parameters and the nonparametric part in partially linear quantile regression models with responses that are missing at random. First, we extend the normal approximation (NA)-based methods of Sun ( 2005 ) to the missing data case. However, the asymptotic covariance matrices of NA-based methods are difficult to estimate, which complicates inference. To overcome this problem, alternatively, we propose the smoothed empirical likelihood (SEL)-based methods. We define SEL statistics for the parameters and the nonparametric part and demonstrate that the limiting distributions of the statistics are Chi-squared distributions. Accordingly, confidence regions can be obtained without the estimation of the asymptotic covariance matrices. Monte Carlo simulations are conducted to evaluate the performance of the proposed method. Finally, the NA- and SEL-based methods are applied to real data. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Xiaofeng Lv & Rui Li, 2013. "Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 317-347, October.
  • Handle: RePEc:spr:alstar:v:97:y:2013:i:4:p:317-347
    DOI: 10.1007/s10182-013-0210-4
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    References listed on IDEAS

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    1. repec:kap:jecinq:v:15:y:2017:i:2:d:10.1007_s10888-017-9348-8 is not listed on IDEAS
    2. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 0. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 0, pages 1-22.
    3. Peixin Zhao & Xinrong Tang, 2016. "Imputation based statistical inference for partially linear quantile regression models with missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 991-1009, November.

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