Uniform asymptotic normality for the Bernoulli scheme

Volume 34 / 2007

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


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.


  • Wojciech NiemiroFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    87-100 Toru/n, Poland
  • Ryszard Zieli/nskiInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 21
    00-956 Warszawa, Poland

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