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Empirical likelihood for linear regression models with missing responses

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  • Qin, Yongsong
  • Li, Ling
  • Lei, Qingzhu

Abstract

To make inference on in a linear regression model with missing responses, Wang and Rao [Wang, Q., Rao, J.N.K., 2001. Empirical likelihood for linear regression models under imputation for missing responses. Canad. J. Statist. 29, 597-608.] constructed an empirical likelihood (EL) statistic based on the 'complete' data set after linear regression imputation which is asymptotically a sum of weighted variables with unknown weights. In this paper, we use a new method to produce a 'complete' data set for Y. Based on this data set, we construct an EL statistic on [beta], and show that the EL statistic has the limiting distribution of which is used to construct confidence region on [beta] without adjustment. Results of a simulation study on the finite sample performance of EL-based confidence region on [beta] are reported.

Suggested Citation

  • Qin, Yongsong & Li, Ling & Lei, Qingzhu, 2009. "Empirical likelihood for linear regression models with missing responses," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1391-1396, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:11:p:1391-1396
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    References listed on IDEAS

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    1. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    2. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    3. Qihua Wang & J. N. K. Rao, 2002. "Empirical Likelihood‐based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 563-576, September.
    4. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
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    2. Peixin Zhao & Liugen Xue, 2013. "Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 380-396, February.
    3. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    4. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    5. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "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. 15(2), pages 195-216, June.
    6. Brady Ryan & Ananthika Nirmalkanna & Candemir Cigsar & Yildiz E. Yilmaz, 2023. "Evaluation of Designs and Estimation Methods Under Response-Dependent Two-Phase Sampling for Genetic Association Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 510-539, July.

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