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The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles. [ABSTRACT FROM AUTHOR]

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures. [ABSTRACT FROM AUTHOR]

This paper studies quantile regression for spatial panel data models with varying coefficients, taking the time and location effects of the impacts of the covariates into account, i.e., the implications of covariates may change over time and location. Smoothing methods are employed for approximating varying coefficients, including B-spline and local polynomial approximation. A fixed-effects quantile regression (FEQR) estimator is typically biased in the presence of the spatial lag variable. The wild bootstrap method is employed to attenuate the estimation bias. Simulations are conducted to study the performance of the proposed method and show that the proposed methods are stable and efficient. Further, the estimators based on the B-spline method perform much better than those of the local polynomial approximation method, especially for location-varying coefficients. Real data about economic development in China are also analyzed to illustrate application of the proposed procedure. [ABSTRACT FROM AUTHOR]

The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure. [ABSTRACT FROM AUTHOR]

This paper studies variable selection for the data set, which has heavy-tailed distribution and high correlations within blocks of covariates. Motivated by econometric and financial studies, we consider using quantile regression to model the heavy-tailed distribution data. Considering the case where the covariates are high dimensional and there are high correlations within blocks, we use the latent factor model to reduce the correlations between the covariates and use the conquer to obtain the estimators of quantile regression coefficients, and we propose a consistency strategy named factor-augmented regularized variable selection for quantile regression (Farvsqr). By principal component analysis, we can obtain the latent factors and idiosyncratic components; then, we use both as predictors instead of the covariates with high correlations. Farvsqr transforms the problem from variable selection with highly correlated covariates to that with weakly correlated ones for quantile regression. Variable selection consistency is obtained under mild conditions. Simulation study and real data application demonstrate that our method is better than the common regularized M-estimation LASSO. [ABSTRACT FROM AUTHOR]