Robust estimation and bias-corrected empirical likelihood in generalized linear models with right censored data

AbstractIn this paper, we study the robust estimation and empirical likelihood for the regression parameter in generalized linear models with right censored data. A robust estimating equation is proposed to estimate the regression parameter, and the resulting estimator has consistent and asymptotic normality. A bias-corrected empirical log-likelihood ratio statistic of the regression parameter is constructed, and it is shown that the statistic converges weakly to a standard χ2 distribution. The result can be directly used to construct the confidence region of regression parameter. We use the bias correction method to directly calibrate the empirical log-likelihood ratio, which does not need to be multiplied by an adjustment factor. We also propose a method for selecting the tuning parameters in the loss function. Simulation studies show that the estimator of the regression parameter is robust and the bias-corrected empirical likelihood is better than the normal approximation method. An example of a real dataset from Alzheimer's disease studies shows that the proposed method can be applied in practical problems.Keywords: Generalized linear modelright censored datarobust estimationempirical likelihoodregression parameter AcknowledgmentsThe authors thank the Editor, Associate Editor and two referees for their helpful comments. The dataset used was provided by Dr. Chunling Liu of the Hong Kong Polytechnic University. The source of this dataset is available on https://adni.loni.usc.edu/about/.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research were supported by the National Natural Science Foundation of China (11971001), the Natural Science Foundation of Henan (222300420417), and the Science and Technology Project (2103004).