- Tytuł:
- An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes
- Autorzy:
- Dudziński, Marcin
- Powiązania:
- https://bibliotekanauki.pl/articles/747144.pdf
- Data publikacji:
- 2017
- Wydawca:
- Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
- Tematy:
-
Almost sure central limit theorem
weak dependence
empirical processes
copulas - Opis:
- Let: \(\mathbf{Y=}\left( \mathbf{Y}_{i}\right)\), where \(\mathbf{Y}_{i}=\left( Y_{i,1},...,Y_{i,d}\right)\), \(i=1,2,\dots \), be a \(d\)-dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf \(F\), and \(F_{n}\left( \mathbf{x}\right) :=\frac{1}{n}\sum_{i=1}^{n}\mathbb{I}\left(Y_{i,1}\leq x_{1},\dots ,Y_{i,d}\leq x_{d}\right)\) denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process \(B_{n}=\sqrt{n}\left( F_{n}-F\right)\) under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.
- Źródło:
-
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 1
0365-1029
2083-7402 - Pojawia się w:
- Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł