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Title: Variable selection in quantile varying coefficient models with heteroscedastic error Authors:  Anneleen Verhasselt - Hasselt University (Belgium) [presenting]
Mohammed Abdulkerim Ibrahim - Hasselt University (Belgium)
Abstract: Quantile regression is a great tool to get a thorough view of the relationship between (the distribution of) a response and covariates. We consider a location-scale quantile varying coefficient model with heteroscedastic error to model longitudinal data. In a longitudinal data setting, it is intuitive to allow the coefficients in the varying coefficient model to vary over time. The functional coefficients are estimated with penalized B-splines. As we allow for heteroscedasticity, the covariates can influence various quantiles of the response differently. Therefore, the problem of variable selection in quantile regression is more challenging. We consider grouped lasso and nonnegative garrote to perform variable selection in the location as well as the scale. When the problem is high-dimensional a two-stage approach, with a first screening stage (independence screening) is used, before applying grouped lasso or nonnegative garrote in the second stage.