Title: Variable selection in quantile varying coefficient models with heteroscedastic error
Authors: Mohammed Abdulkerim Ibrahim - Hasselt University (Belgium) [presenting]
Anneleen Verhasselt - Hasselt University (Belgium)
Abstract: Quantile regression gives a thorough view of the relationship of the covariates with the entire distribution of the response. Varying coefficient models are considered, allowing the coefficients vary with time in a longitudinal data setting. Since important variables can influence various quantiles in different ways, the problem of variable selection in quantile regression is more challenging. We propose an easy way to check the influence of the covariates on the distribution of the response by investigating both the location and the scale. The functions are estimated with Penalized B-splines. A grouped Adaptive Lasso and nonnegative garrote are considered for variable selection. The selection procedures have consistency in variable selection under suitable conditions. Further, the estimated functional coefficients are shown to have an optimal convergence rate to the true functional coefficients. Our simulation study shows that both methods have good performance with respect to both the location and the scale in selecting the important covariates as well as in estimating the functional coefficients. The procedures are compared with grouped adaptive Lasso using B-splines estimation and group SCAD. Nonnegative garrote outperforms the other methods way far with respect to the computational time. Finally, the procedures are illustrated on two real-data examples.