1Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toru/n, Poland 2Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland
Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 215-221
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.
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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author = {Wojciech Niemiro and Ryszard Zieli/nski},
title = {Uniform asymptotic normality
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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
