NONPARAMETRIC LEAST SQUARES ESTIMATION OF A MULTIVARIATE CONVEX REGRESSION FUNCTION

作者：Seijo Emilio^*; Sen Bodhisattva

来源：Annals of Statistics, 2011, 39(3): 1633-1657.

DOI：10.1214/10-AOS852

• Consistency
• linear program
• semidefinite quadratic program
• shape restricted estimation
• subdifferentials

This paper deals with the consistency of the nonparametric least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided.

• 出版日期2011-6