An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

• Autorzy: Marcin Dudziński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Almost sure central limit theorem; weak dependence; empirical processes; copulas

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2017
• Tom: 71
• Numer: 1

Daty

wydano

2017

online

2017-06-30

Twórcy

autor

Marcin Dudziński

Bibliografia

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Identyfikatory

DOI

10.17951/a.2017.71.1.11