Geodesic
Uniform asymptotic normality for the Bernoulli scheme
Wojciech Niemiro1 ; Ryszard Zieli/nski2
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toru/n, Poland
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland
Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 215-221.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is easy to notice that no sequence of estimators of the probability of success $\theta$ in a Bernoulli scheme can converge (when standardized) to $N(0,1)$ uniformly in $\theta\in ]0,1[$. We show that the uniform asymptotic normality can be achieved if we allow the sample size, that is, the number of Bernoulli trials, to be chosen sequentially.
DOI : 10.4064/am34-2-6
Keywords: easy notice sequence estimators probability success theta bernoulli scheme converge standardized uniformly theta uniform asymptotic normality achieved allow sample size number bernoulli trials chosen sequentially

Wojciech Niemiro 1 ; Ryszard Zieli/nski 2

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toru/n, Poland
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland 
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Wojciech Niemiro; Ryszard Zieli/nski. Uniform asymptotic normality
 for the Bernoulli scheme. Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 215-221. doi : 10.4064/am34-2-6. http://geodesic.mathdoc.fr/articles/10.4064/am34-2-6/

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