In this article we highlight the main differences of available methods for the analysis of regression functions that are probably additive separable. We first discuss definition and interpretation of the most common estimators in practice. This is done by explaining the different ideas of...

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically...

In this paper we present a detailed numerical comparison of three monotone nonparametric kernel regression estimates, which isotonize a nonparametric curve estimator. The first estimate is the classical smoothed isotone estimate of Brunk (1958). The second method has recently been proposed by...

A monotone estimate of the conditional variance function in a heteroscedastic, nonpara- metric regression model is proposed. The method is based on the application of a kernel density estimate to an unconstrained estimate of the variance function and yields an esti- mate of the inverse variance...

In this note we consider several goodness-of-fit tests for model specification in non- parametric regression models which are based on kernel methods. In order to circumvent the problem of choosing a bandwidth for the corresponding test statistic we propose to consider the statistics as...

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...

In the common nonparametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes obtained from the standardized nonparametric residuals under the null hypothesis (of...

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...