We consider the smoothness parameter s*(f) of a function f∈L2(R) in terms of Besov spaces. The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0

In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter ). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness...

When system parameters vary at a fast rate, identification schemes based on model-free local estimation approaches do not yield satisfactory results. In cases like this, more sophisticated parameter tracking procedures must be used, based on explicit models of parameter variation (often referred to as hypermodels), either deterministic or stochastic. Kalman filter trackers, which belong to the second category, are seldom used in...

The problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...

The smoothness and flexibility of distribution of goods by containers are teh most important impulses for the development in these means of transport. But the second main reason for the growing containerization of freifht is cargo safety.