In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A new basis for the space of natural splines is derived, and the local minimax property for these splines is used to derive two...

In this article a new monotone nonparametric estimate for a regression function of two or more variables is proposed. The method starts with an unconstrained nonparametric regression estimate and uses successively one-dimensional isotonization procedures. In the case of a strictly monotone...

A new nonparametric estimate of a convex regression function is proposed and its stochastic properties are studied. The method starts with an unconstrained estimate of the derivative of the regression function, which is firstly isotonized and then integrated. We prove asymptotic normality of the...