Empirical likelihood inference for median regression models for censored survival data

Empirical likelihood methods based on influence functions

“…where 12 and 22 are consistent estimators for A 12 and A 22 , respectively. The proposed constraint is defined to be…”

“…This so-called plugged-in empirical likelihood method has been widely applied under various semiparametric models by much literature. For example, [14,17] on partially linear models, [11] on Cox models, [10,5] on censored linear models, [12] on censored quantile models, [21,26] on signle-index models, [6,24] on linear transformation models, [18,19] on linear models with missing responses, among many others.…”

“…In many cases, instead of converging to a chi-squared distribution, the log-empirical likelihood ratios with estimators being plugged in converge to a weighted sum of several independent chi-squared distributions, c.f. [10,18,19,5,12,21,26,6,24], etc. The weights, depending on the limiting variances of the estimators for parameters of interest, are unknown.…”

A review on empirical likelihood methods for regression

“…In addition, assume that the censoring variable C i is independent of the vector of covariates X i . For this model, Qin and Tsao (2003) considered the following EL ratio, based on the likelihood for complete data :…”

Empirical likelihood inference for censored median regression with weighted empirical hazard functions

“…More recently, Qin and Tsao (2003) developed EL based confidence region based on estimating equation of Ying et al (1995). One advantage is that the EL based confidence region is determined by the data set.…”