The purpose of this paper is to propose a procedure for testing the equality of several regression curves fi in nonparametric regression models when the noise is inhomogeneous. This extends work of Dette and Neumeyer (2001) and it is shown that the new test is asymptotically uniformly more...

Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + sigma (t,Xt) dWt are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the...

This paper deals with the problem of the discrimination between stable and unstable time series. One criterion for the seperation is given by the size of the Lyapunov exponent, which was originally defined for deterministic systems. However, this paper will show, that the Lyapunov exponent can...

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 compare data from BTA deep-hole drilling experiments conducted according to an experimental design, which had to be repeated due to the development of spiralling in all experiments in the first repetition. We compare the time series of the drilling torque and the bending moment...

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...

We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters...

We discuss moving window techniques for fast extraction of a signal comprising monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust...

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 paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its associated sequential partial sum process under...