Imputed Empirical Likelihood for Varying Coefficient Models with Missing Covariates

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The empirical likelihood-based inference for varying coefficient models with missing covariates is investigated. An imputed empirical likelihood ratio function for the coefficient functions is proposed, and it is shown that iis limiting distribution is standard chi-squared. Then the corresponding confidence intervals for the regression coefficients are constructed. Some simulations show that the proposed procedure can attenuate the effect of the missing data, and performs well for the finite sample.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

P. Zhao, "Imputed Empirical Likelihood for Varying Coefficient Models with Missing Covariates," Open Journal of Applied Sciences, Vol. 3 No. 1B, 2013, pp. 44-48. doi: 10.4236/ojapps.2013.31B1009.

 [1] Q. H. Wang and J. N. K. Rao, “Empirical Likelihood for Linear Models under Imputation for Missing Responses,” The Canadian Journal of Statistics, Vol. 29, No. 4，2001, pp. 597-608 . doi：10.2307/3316009 [2] L. G. Xue, “Empirical Likelihood for Linear Models with Missing Responses,” Journal of Multivariate Analysis, Vol. 100, No. 7,2009, pp. 1353-1366. doi：10.1016/j.jmva.2008.12.009 [3] Q. H. Wang, “Statistical Estimation in Partial Linear Models with Covariate Data Missing at Random,” Annals of the Institute of Statistical Mathematics, Vol. 61, No. 1, 2009, pp. 47-84. doi:10.1007/s10463-007-0137-1 [4] H. Liang, S. J. Wang, J. M. Robbins and R. J. Carroll, “Estimation in Partially Linear Models with Missing Covariates,” Journal of the American Statistical Association, Vol. 99, No. 466, 2004, pp. 357-367. doi：10.1198/016214504000000421 [5] H. Wong, S. J. Guo, M. Chen and W.C. IP, “On Locally Weighted Estimation and Hypothesis Testing of Varying Coefficient Models with Missing Covariates,” Journal of Statistical Planning and Inference, Vol. 139, No. 9, No. 1, 2009, pp. 2933-2951. doi：10.1016/j.jspi.2009.01.016 [6] A. B. Owen, “Empirical Likelihood Ratio Confidence Regions,” The Annals of Statistics, Vol. 18, No. 1, 1990, pp. 90-120. doi：10.1214/aos/1176347494 [7] L. G. Xue and L. X. Zhu, “Empirical Likelihood for a Varying Coefficient Model with Longitudinal Data,” Journal of the American Statistical Association, Vol. 102, No. 478, 2007, pp. 642-654. doi：10.1198/016214507000000293 [8] P. X. Zhao and L. G. Xue, “Variable Selection for Semiparametric Varying Coefficient Partially Linear Models with Missing Response at Random,” Acta Mathematica Sinica, English Series, Vol. 27, No. 11, 2011, pp. 2205-2216. doi：10.1007/s10114-011-9200-1