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

Mary C. Meyer and Xiyue Liao

Journal of Nonparametric Statistics, 2022, vol. 34, issue 1, 1-21

Abstract: 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.

Date: 2022
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DOI: 10.1080/10485252.2021.2014834

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