Simultaneous Estimation of Multiple Conditional Regression Quantiles

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In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous variety for the quantile level over (0,1). As a result, all the quantile curves can be obtained via a 2-dimensional surface simultaneously. Most importantly, the proposed minimizing criterion can be readily transformed to a linear programming problem. We use tensor product bi-linear quantile smoothing B-splines to fit it. The asymptotic property of the estimator is derived and a real data set is analyzed to demonstrate the proposed method.