Uniform asymptotic normality for the Bernoulli scheme

• Autorzy: Wojciech Niemiro , Ryszard Zieliński
• Języki publikacji: EN

Abstrakty

EN

It is easy to notice that no sequence of estimators of the probability of success θ in a Bernoulli scheme can converge (when standardized) to N(0,1) uniformly in θ ∈ ]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.

Kategorie tematyczne

• 62L12: Sequential estimation
• 60B10: Convergence of probability measures
• 60F05: Central limit and other weak theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2007
• Tom: 34
• Numer: 2
• Strony: 215-221

Daty

wydano

2007

Twórcy

autor

Wojciech Niemiro

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, 87-100 Toruń, Poland

autor

Ryszard Zieliński

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/am34-2-6