Abstract:Functional quantile regression performs well in many practical applications, especially when dealing with data with complex dependency structures, where the conditional quantile relationship between scalar response variables and functional predictor variables is often considered. For the regression models of functional data, existing algorithms rely on approximating the slope function by adopting the functional principal component basis and then performing estimation based on this approximation. This study proposes an algorithm designed for functional quantile regression, which can enhance estimation efficiency and reduce prediction errors. The proposed algorithm introduces a functional eigen-sparse envelope space to concentrate the information set of functional predictor variables for quantile regression in a smaller space, thereby effectively lowering the complexity of the functional quantile regression model. Subsequently, the quantile regression model after information concentration is estimated by employing the generalized method of moments (GMM). The experimental results demonstrate that the proposed algorithm outperforms the comparison algorithms on public functional datasets CanadianWeather and wheat.