Abstract
This article proposes a new approach for variable selection in the single index quantile regression model. Compared to existing methods, the new approach produce sparse solutions for the index vector. Performance of the new method is enhanced by a fully adaptive penalty function. Finite sample performance is studied through a simulation study that compares the proposed method with existing work under several criteria. A data analysis is given which highlights the usefulness of the proposed methodology.
Highlights
With the advances in data generation, collection, and storage, modeling data with large number of covariates has become the rule rather than the exception
This article proposes a new approach for variable selection in the single index quantile regression model
In this article we examine the estimation and variable selection of the single-index quantile regression model
Summary
With the advances in data generation, collection, and storage, modeling data with large number of covariates has become the rule rather than the exception. In the context of nonparametric regression, handling this issue becomes an extremely challenging task, because data sparseness in local neighborhoods makes it virtually impossible to perform a fully nonparametric estimation of a regression function with multiple covariates. To overcome this issue Ichimura (1990) proposed the single-index model. As a result the estimates becomes highly sensitive to extreme values To overcome these difficulties and allow the estimation of various conditional quantiles of the response variable, Koenker & Bassett (1978) in their pioneering work introduced the quantile regression framework. In this article we examine the estimation and variable selection of the single-index quantile regression model
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