We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a...

In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function is considered. Recently Dette and Hetzler (2008) proposed a test statistic, which is based on an empirical process of pseudo residuals. The process converges weakly to a...

We construct optimal designs for estimating fetal malformation rate, prenatal death rate and an overall toxicity index in a toxicology study under a broad range of model assumptions. We use Weibull distributions to model these rates and assume that the number of implants depend on the dose...

In the common Fourier regression model we investigate the optimal design problem for estimating pairs of the coefficients, where the explanatory variable varies in the interval [¡¼; ¼]. L-optimal designs are considered and for many important cases L-optimal designs can be found explicitly,...

In nonparametric curve estimation, the smoothing parameter is critical for performance. In order to estimate the hazard rate, we compare nearest neighbor selectors that minimize the quadratic, the Kullback-Leibler, and the uniform loss. These measures result in a rule of thumb, a...

We propose a general bootstrap procedure to approximate the null distribution of nonparametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy to verify conditions, we establish asymptotic validity of the proposed bootstrap procedure....

To estimate the effective dose level ED a in the common binary response model, several parametric and nonparametric estimators have been proposed in the literature. In the present paper, we focus on nonparametric methods and present a detailed numerical comparison of four different approaches to...

Toxicologists have been increasingly using a class of models to describe a continuous response in the last few years. This class consists of nested nonlinear models and is used for estimating various parameters in the models or some meaningful function of the model parameters. Our work here is...