An application of the Bernoulli part to local limit theorems for moving averages on stationary sequences

Autor:	David McDonald, André Robert Dabrowski
Rok vydání:	1996
Předmět:	Statistics and Probability Pure mathematics Bernoulli's principle Moving average Mathematical analysis Limit (mathematics) Statistics Probability and Uncertainty Random variable Central limit theorem Mathematics
Zdroj:	Canadian Journal of Statistics. 24:293-305
ISSN:	1708-945X 0319-5724
DOI:	10.2307/3315740
Popis:	We consider partial sums Sn of a general class of stationary sequences of integer-valued random variables, and we provide sufficient conditions for Sn to satisfy a local limit theorem. To prove this result, we introduce a concept called the Bernoulli part. The amount of Bernoulli part in Sn determines the extent to which the density of Sn is relatively flat. If in addition Sn satisfies a global central limit theorem, the local limit theorem follows. Nous considerons les sommes partielles, Sn, d'une classe generale de sequences stationnaires de variables aleatoires B valeurs entieres et nous fournissons des conditions suffisantes pour que Sn satisfasse a un theoreme limite local. Afin de demontrer ce resultat, nous presentons un concept nomme la composante Bernoulli. La quantite de composante Bernoulli dans Sn determine dans quelle mesure la densite de Sn est relativement plate. Si, de plus, Sn satisfait a un theoreme limite central global, le theoreme limite local ensuit.
Databáze:	OpenAIRE
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