Michael H. Neumann

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We suppose that a Lévy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the Lévy-Khinchine characteristics as the number of observations tends to infinity, keeping the observation distance fixed. For a specific C 2-criterion this estimator is rate-optimal. The(More)
We derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors. We construct, on a suuciently rich probability space, such a pairing of the random variables of both experiments that the set of observations fX 1 ; : : : ; X n g from the time series model is nearly the(More)
New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that of the model class postulated under the null hypothesis. The model specification under the null allows for Markovian(More)
We derive minimax rates for estimation in anisotropic smoothness classes. These rates are attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension. It is shown that this basis is superior to its one-scale multiresolution analog, if different degrees of smoothness in diierent(More)
Wavelets have motivated development of a host of new ideas in nonparametric regression smoothing. Here we apply the tool 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(More)
New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that of the model class postulated under the null hypothesis. The model specification under the null allows for Markovian(More)
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from(More)