Estimation and inference for partial linear regression surfaces using monotone warped-plane splines

Methods are proposed for spline estimation of monotone regression surfaces, without additivity assumptions and allowing for linear covariate effects. The surfaces are estimated by a continuous piece-wise warped-plane spline with linear inequality constraints. Surface and covariate effects are estimated simultaneously with cone projection, leading to useful inference methods. For surfaces in two predictors, a cube-root convergence rate is attained, and conditions for square-root convergence of the linear terms are derived. Point-wise confidence intervals for the surfaces incorporate mixtures of covariance matrices, with the mixing parameters estimation by simulations. The methods are implemented in the R package cgam.