Browsing by Subject "almost periodic functions"

Now showing 1 - 3 of 3

Access status: Restricted ,
Bootstrap w prawie okresowych szeregach czasowych
(Data obrony: 2014-09-22) Uzar, Jakub
Wydział Matematyki Stosowanej
Access status: Open Access ,
Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm
(Wydawnictwa AGH, 2021) Boulahia, Fatiha; Hassaine, Slimane
In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.
Access status: Open Access ,
Metody resamplingowe w dziedzinie czasu dla niestacjonarnych szeregów czasowych o strukturze okresowej i prawie okresowej
(2007-03-22) (Data obrony: 2008) Synowiecki, Rafał
Wydział Matematyki Stosowanej
The main objective of the thesis is to establish conditions for consistency of resampling methods in the area of alpha-mixing time series with periodic and almost periodic structure. This kind of nonstationary data are gathered in many areas such as climatology, economy or telecommunications. For (almost) periodic time series statistical inference regarding e.g. autocovariance function is based on its Fourier representation. This thesis considers four types of resampling techniques, known in the literature. The focus here is to investigate these techniques in the general almost periodic setup. The first procedure is called subsampling. It consists inrecalculating estimator over every possible subseries of some length. It is shown that the estimator of Fourier coefficient needs some modification for the subsampling to be consistent. The second method is moving block bootstrap. For this method sample mean is the starting point. Then some corollaries are evaluated. They regard multivariate case, smooth functions of the mean and estimators of Fourier coefficients. The two remaining procedures are seasonal block bootstrap and periodic block bootstrap. In order to apply them one needs to know the exact length of the period. The first of the two aforementioned methods is consistent under general assumptions similar to moving block bootstrap context. The other is shown to work only in the case of triangular random arrays with the period increasing row-wise.