Quantile Regression with Shape-Constrained Varying Coefficients

摘要: Although much research has been devoted to shape-constrained function estimation, the efforts have practically confined case of univariate smoothing where unknown is a single variable. We extend estimation general class constrained nonparametric or semi-parametric regression component can be described by one-dimensional smooth functions. Built on ideas He and Shi (1998) Ng (1999), we consider quantile with shape coefficient B-splinesare used approximate functions, constrain ts are imposed spline coefficients. The method implemented w ith any existing linear program knot selection algorithm. show that does not compromise smoothness estimators, flexibility model computational efficiency. Asymptotic results con strained B-spline estimators same rate convergence normal limiting distribution as unconstrained estimators. accommodate linearizable constraints such convexity/concavity, monotonicity, periodicity pointwise constraints.