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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 develop a method of estimating change{points of a function in the case of indirect noisy observations. As two paradigmatic problems we consider de-convolution and errors-in-variables regression. We estimate the scalar products of our indirectly observed function with appropriate test functions, which are shifted over the interval of interest. An… (More)

1 1 1. Introduction Autoregressive models form an important class of processes in time series analysis. A nonparametric version of these models was introduced by Jones (1978). To allow for heteroscedastic modelling of the innovations, people often consider the model where the " t are assumed to be i.i.d. with mean 0 and variance 1. Several authors dealt… (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)

- MICHAEL H. NEUMANN, EFSTATHIOS PAPARODITIS
- 2008

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)

- Michael H Neumann, Rainer Von Sachs
- 1997

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)

- J S M Marron, M H Neumann, P And Patil
- 1995

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)

- Michael H. Neumann, Efstathios Paparoditis
- 2005

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)

We consider nonparametric estimation of the parameter functions a i () , i = 1; : : : ; p , of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a i , the empirical wavelet coeecients are derived from the time series data as the solution of a least squares minimization problem. In order to allow the… (More)