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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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

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