Geodesic
Uniform asymptotic normality for the Bernoulli scheme
Wojciech Niemiro 1   ; Ryszard Zieli/nski 2
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toru/n, Poland
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland
Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 215-221 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/am34-2-6
Keywords: easy notice sequence estimators probability success theta bernoulli scheme converge standardized uniformly theta uniform asymptotic normality achieved allow sample size number bernoulli trials chosen sequentially

Wojciech Niemiro  1   ; Ryszard Zieli/nski  2

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toru/n, Poland
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland 
@article{10_4064_am34_2_6,
     author = {Wojciech Niemiro and Ryszard Zieli/nski},
     title = {Uniform asymptotic normality
 for the {Bernoulli} scheme},
     journal = {Applicationes Mathematicae},
     pages = {215--221},
     year = {2007},
     volume = {34},
     number = {2},
     doi = {10.4064/am34-2-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am34-2-6/}
}
TY  - JOUR
AU  - Wojciech Niemiro
AU  - Ryszard Zieli/nski
TI  - Uniform asymptotic normality
 for the Bernoulli scheme
JO  - Applicationes Mathematicae
PY  - 2007
SP  - 215
EP  - 221
VL  - 34
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am34-2-6/
DO  - 10.4064/am34-2-6
LA  - en
ID  - 10_4064_am34_2_6
ER  - 
%0 Journal Article
%A Wojciech Niemiro
%A Ryszard Zieli/nski
%T Uniform asymptotic normality
 for the Bernoulli scheme
%J Applicationes Mathematicae
%D 2007
%P 215-221
%V 34
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/am34-2-6/
%R 10.4064/am34-2-6
%G en
%F 10_4064_am34_2_6
Wojciech Niemiro; Ryszard Zieli/nski. Uniform asymptotic normality
 for the Bernoulli scheme. Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 215-221. doi: 10.4064/am34-2-6

Cité par Sources :