Michael H. Neumann

The significance of entry routes as point and non-point sources of pesticides in small streams

In an agricultural catchment area in Germany we analyzed water samples from five entry routes for 2 insecticides. 5 fungicides and 13 herbicides. The sewage plant outlet and the emergency overflow of a sewage sewer contained only herbicides. In each farmyard runoff we found on average 24 g pesticides during application period, presumably caused by cleaning the spraying equipment. In comparison, the field runoff and the rainwater sewer contained less load, but also insecticides, fungicides and herbicides. The sewage plant caused 65.9% of the total herbicide load, the sewage sewer 19.8% and the farmyard runoff 12.8%. The farmyards also caused 83.7% of total insecticide and 83.8% of fungicide load. The total load of all entry routes is correlated with the amount of pesticides applied in the catchment area and the Ko/w value for each pesticide (mult. regress. r2: 0.82; p<0.0001; n = 14). In stream A the sewage plant caused a slight but continuous contamination by herbicides with 82% of the total load found during low-water phases. In comparison, stream B had only farmyard runoff and non-point sources, which caused high peaks of herbicide and a contamination by insecticides. Consequently, high-water phases generated 70% of the total pesticide load.

On the effect of estimating the error density in nonparametric deconvolution

It is quite common in the statistical literature on nonparametric deconvolution to assume that the error density is perfectly known. Since this seems to be unrealistic in many practical applications, we study the effect of estimating the unknown error density. We derive minimax rates of convergence and propose a modification of the usual kernel-based estimation scheme, which takes the uncertainty about the error density into account. A simulation study quantifies the possible gains by this new method in finite sample situations.

Absolute regularity and ergodicity of Poisson count processes

We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that the stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.

A wavelet-based test for stationarity

We develop a test for stationarity of a time series against the alternative of a time-changing covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time-varying spectral density. Coefficients w.r.t. a Haar wavelet series expansion of such a time-varying periodogram are a possible indicator whether there is some deviation from covariance stationarity. We propose a test based on the limit distribution of these empirical coefficients.

Exact Risk Analysis of Wavelet Regression

Abstract Wavelets have motivated development of a host of new ideas in nonparametric regression smoothing. Here we apply the too] of exact risk analysis, to understand the small sample behavior of wavelet estimators, and thus to check directly the conclusions suggested by asymptotics. Comparisons between some wavelet bases, and also between hard and soft thresholding, are given from several viewpoints. Our results provide insight as to why the viewpoints and conclusions of Donoho and Johnstone differ from those of Hall and Patil.

A method for monitoring pesticides bound to suspended particles in small streams

A Suspended Particle Sampler (SPS) is described with which pesticides bound to suspended particles can be readily monitored in small streams. Retention of the grain-size fraction below 0.02 mm grain diameter depends on the velocity of flow through the device, averaging 50% for 0.05 m s−1 and 15% for 0.41 m s−1. The advantage of the SPS lies in its simple, economical construction and in the slight expenditure of time and effort needed to use it. Comparison with other methods of monitoring short-term pesticide contamination shows that the contamination values provided by the SPS describe the actual contamination dynamics considerably better than do the data obtained by conventional sampling of suspended sediments.

Problems related to confidence intervals for impulse responses of autoregressive processes

Confidence intervals for impulse responses computed from autoregressive processes are considered. A detailed analysis of the methods in current use shows that they are not very reliable in some cases. In particular, there are theoretical reasons for them to have actual coverage probabilities which deviate considerably from the nominal level in some situations of practical importance. For a simple case alternative bootstrap methods are proposed which provide correct results asymptotically.

Simultaneous bootstrap confidence bands in nonparametric regression

In the present paper we construct asymptotic confidence bands in non-parametric regression. Our assumptions cover unequal variances of the observations and nonuni-form, possibly considerably clustered design. The confidence band is based on an undersmoothed local polynomial estimator. An appropriate quantile is obtained via the wild bootstrap. We derive certain rates (in the sample size n) for the error in coverage probability, which improves on existing results for methods that rely on the asymptotic distribution of the maximum of some Gaussian process. We propose a practicable rule for a data-dependent choice of the band-width. A small simulation study illustrates the possible gains by our approach over alternative frequently used methods.

Fully Data-Driven Nonparametric Variance Estimators

We consider the problem of estimating the unknown variance function υ in a nonparametric regression model. As a basis for our estimators we take estimated residuals which are based on a kernel estimator of the mean vector. Then we form with these residuals a kernel estimator of υ. Main emphasis is on a data-driven choice of the bandwidths involved in the procedure. It is shown that the risk of this estimator attains the uniform convergence rate in Sobolev classes for υ under weak smoothness assumptions on the mean. Moreover, we prove that there is asymptotically no loss due to the estimation of the mean.

Wavelet Thresholding : Beyond the Gaussian I.I.D. Situation

With this article we first like to a give a brief review on wavelet thresholding methods in non-Gaussian and non-i.i.d. situations, respectively. Many of these applications are based onGaussian approximations of the empirical coefficients. For regression and density estimation with independent observations, we establish joint asymptotic normality of the empirical coefficients by means of strong approximations. Then we describe how one can prove asymptotic normality under mixing conditions on the observations by cumulant techniques.