Marcinkiewicz–Zygmund strong laws for -statistics of weakly dependent observations

Autor:	Olimjon Sh. Sharipov, Herold Dehling
Rok vydání:	2009
Předmět:	Statistics and Probability Law of large numbers Statistics Mixed distribution Statistics Probability and Uncertainty Mathematics
Zdroj:	Statistics & Probability Letters. 79:2028-2036
ISSN:	0167-7152
DOI:	10.1016/j.spl.2009.06.012
Popis:	We prove the Marcinkiewicz–Zygmund Strong Law of Large Numbers for U -statistics of strictly stationary, absolutely regular observations ( ξ i ) i ≥ 1 . Under suitable moment conditions and conditions on the mixing rate, we show that n − 2 + γ ∑ 1 ≤ i j ≤ n ( h ( ξ i , ξ j ) − E h ( ξ , η ) ) → 0 for some γ ≥ 0 , in the non-degenerate case, and n − 1 + γ ∑ 1 ≤ i j ≤ n ( h ( ξ i , ξ j ) − E h ( ξ , η ) ) → 0 in the degenerate case.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5476b6680106f7f0f4457668ab53bf60 https://doi.org/10.1016/j.spl.2009.06.012 Zobrazit plný text záznamu Full Text from ScienceDirect