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...

We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available....

For the Weibull- and Richards-regression model robust designs are determined by maximizing a minimum of D- or D1-efficiencies, taken over a certain range of the non-linear parameters. It is demonstrated that the derived designs yield a satisfactory solution of the optimal design problem for this...

In the common Fourier regression model we determine the optimal designs for estimating the coefficients corresponding to the lower frequencies. An analytical solution is provided which is found by an alternative characterization of c-optimal designs. Several examples are provided and the...

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 this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued...

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...