On uniform consistent estimators for convex regression

FORZANI, L.; P. MORIN; N. AGUILERA

JOURNAL OF NONPARAMETRIC STATISTICS

TAYLOR & FRANCIS LTD

Lugar: Londres; Año: 2011 vol. 23 p. 897 - 908

1048-5252

A new nonparametric estimator of a convex regression function in any dimension is proposed and its uniform convergence properties are studied. We start by using any estimator of the regression function and convexify it by taking the convex envelope of a sample of the approximation obtained. We prove that the uniform rate of convergence of the estimator is maintained after the convexification is applied. The finite-sample properties of the new estimator are investigated by means of a simulation study and the application of the new method is demonstrated in examples.