Weighted quantile regression with missing covariates using empirical likelihood

Variable selection in high-dimensional linear model with possibly asymmetric errors

“…Moreover, the SCAD penalty also allows automatic selection of variables. Still for a quantile linear model with missing covariables of type MAR, Liu and Yuan (2016) estimates and studies the asymptotic properties of a weighted EL estimator. Using a constraint function that does not satisfy the conditions considered in the present paper, how we will see later, Ozdemir and Arsaln (2021) considers a linear model without missing data where the model parameters are estimated by the EL method without penalty.…”

Weighted empirical likelihood for quantile regression with nonignorable missing covariates

“…Although βELW can be obtained easily, it is difficult to estimate the limiting covariance matrix analytically. We apply the resampling method in Liu and Yuan (2016) to the inference about β * .…”

“…Chen et al (2015) examined the problem of estimation in a quantile regression model and developed three nonparametric methods when observations are missing at ran-dom under independent and nonidentically distributed errors. Liu and Yuan (2016) proposed a weighted quantile regression model with weights chosen by empirical likelihood. This approach efficiently incorporates the incomplete data into the data analysis by combining the complete data unbiased estimating equations and incomplete data unbiased estimating equations.…”

On histogram-based regression and classification with incomplete data

“…Although the great majority of the existing literature deals mainly with missingness in response variables, there have also been several results dealing with missing covariate components (which is the setup of this paper). These include Chen et al (2016) who proposed an estimating equation method for logistic partially linear models with missing covariates, Liu and Yuan (2016) who considered the estimation of conditional quantiles with some covariates missing at random, and the results of Lukusa et al (2016) on Poisson regression. Bravo (2015) considered the estimation of a general class of semiparametric models where the nonparametric component of the model is computed iteratively using local linear estimation.…”