Geodesic
Adaptive chi-square tests
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 150-166

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider minimax hypothesis testing problem $H_0$: $f=f_0$, $f_0(x)\equiv 1$ on a distribution density $f$ of i.i.d. observations $X_1,\dots,X_n$, $X_i\in[0,1]$, $n\to\infty$ versus alternative corresponding to smooth densities $f$ which are distant enough from $f_0$. A distance between $f_0$ and $f$ is measured in $L_p$-norm and a smoothness $\sigma$ of $f$ is measured in $L_q$-norm. A priory the values $\sigma,p,q$ are not fixed but satisfy to constraints $1\le p\le 2$, $p\le q$, $\sigma>0$. We show that optimal minimax rate is provided by test procedures which are based on the union of chi-square tests with increasing number of cells. 
@article{ZNSL_1997_244_a9,
     author = {Yu. I. Ingster},
     title = {Adaptive chi-square tests},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--166},
     publisher = {mathdoc},
     volume = {244},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a9/}
}
TY  - JOUR
AU  - Yu. I. Ingster
TI  - Adaptive chi-square tests
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1997
SP  - 150
EP  - 166
VL  - 244
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a9/
LA  - ru
ID  - ZNSL_1997_244_a9
ER  - 
%0 Journal Article
%A Yu. I. Ingster
%T Adaptive chi-square tests
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 150-166
%V 244
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a9/
%G ru
%F ZNSL_1997_244_a9
Yu. I. Ingster. Adaptive chi-square tests. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 150-166. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a9/