# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Uniform asymptotic normality for the Bernoulli scheme

### Tom 34 / 2007

Applicationes Mathematicae 34 (2007), 215-221 MSC: 60F05, 60B10, 62L12. DOI: 10.4064/am34-2-6

#### Streszczenie

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.

#### Autorzy

• Wojciech NiemiroFaculty of Mathematics and Computer Science
Nicolaus Copernicus University
87-100 Toru/n, Poland
e-mail
• Ryszard Zieli/nskiInstitute of Mathematics