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Abstract:
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Modeling quantiles of the distribution of a response variable provides a more comprehensive picture about its behavior. Envelope is a dimension reduction approach that has been proven to provide more efficient parameter estimation compared to the maximum likelihood approach in certain situations. In this paper, we combine the ideas of generalized Huber function, generalized method of moment, and envelope and proposed a new envelope quantile regression. In addition, we employed the adaptive LASSO to select informative variables. The efficacy of this new solution is illustrated through simulation studies and real data analysis.
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