Quantile sheet estimator with shape constraints

A quantile sheet is a global estimator for multiple quantile curves. A quantile sheet estimator is proposed to maintain the non-crossing properties for different quantiles. The proposed estimator utilizes SCOP: shape-constrained P-spline to enforce the non-crossing properties directly in construction. A local GCV parameter tunning algorithm is used for fast estimation results. Data simulation shows the proposed method and existing competitors can recover the underlying quantiles with comparable mean square error.