Deterministic and stochastic approach to modeling common trends has been applied to time series of horizontal coordinates of the permanent GPS station Modra – Piesky (recorded weekly during the period of 4 years).
Nonlinear dynamic processes with time-varying time delays can often be encountered in industry. Time-delay estimation for nonlinear dynamic systems with time-varying time delays is an important issue for system identification. In order to estimate the dynamics of a process, a dynamic neural network with an external recurrent structure is applied in the modeling procedure. In the case where a delay is time varying, a useful way is to develop on-line time-delay estimation mechanisms to track the time-delay...
It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c1 and c2 such that c2≈1.01 c1. A discussion of relative merits of this result versus limit theorems is given.
The problem of testability has been undertaken many times in the context of linear hypotheses. Almost all these considerations restricted to some algebraical conditions without reaching the nature of the problem. Therefore, a general and commonly acceptable notion of testability is still wanted. Our notion is based on a simple and natural decision theoretic requirement and is characterized in terms of the families of distributions corresponding to the null and the alternative hypothesis. Its consequences...
We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure L0(G) of the boundary of a set G ⊂ ℝd (with d ≥ 2) can be formally defined, via a simple limit, by the so-called Minkowski content. We study the estimation of L0(G) from a sample of random points inside and outside G. The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to G. Under this design we suggest a simple nonparametric...
Many complex systems occurring in various application share the property that the underlying Markov process remains in certain regions of the state space for long times, and that transitions between such metastable sets occur only rarely. Often the dynamics within each metastable set is of minor importance, but the transitions between these sets are crucial for the behavior and the understanding of the system. Since simulations of the original process are usually prohibitively expensive, the effective...
Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.
We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. [10] and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite-sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included.