Uniform asymptotic normality for the Bernoulli scheme
Volume 34 / 2007
Applicationes Mathematicae 34 (2007), 215-221
MSC: 60F05, 60B10, 62L12.
DOI: 10.4064/am34-2-6
Abstract
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.
