Uniform asymptotic normality for the Bernoulli scheme

Wojciech Niemiro, and Ryszard Zieliński. "Uniform asymptotic normality for the Bernoulli scheme." Applicationes Mathematicae 34.2 (2007): 215-221. <http://eudml.org/doc/279699>.

@article{WojciechNiemiro2007,
abstract = {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.},
author = {Wojciech Niemiro, Ryszard Zieliński},
journal = {Applicationes Mathematicae},
keywords = {central limit theorem; uniform central limit theorem; Bernoulli scheme; stopping times; sequential estimators},
language = {eng},
number = {2},
pages = {215-221},
title = {Uniform asymptotic normality for the Bernoulli scheme},
url = {http://eudml.org/doc/279699},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Wojciech Niemiro
AU - Ryszard Zieliński
TI - Uniform asymptotic normality for the Bernoulli scheme
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 2
SP - 215
EP - 221
AB - 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.
LA - eng
KW - central limit theorem; uniform central limit theorem; Bernoulli scheme; stopping times; sequential estimators
UR - http://eudml.org/doc/279699
ER -