Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 62G10 Hypothesis testing
- 62H10 Distribution of statistics
- 62H15 Hypothesis testing

**Résumé:** We test whether two independent samples of i.i.d.
random variables
$X_1,\ldots,X_n$ and $Y_1,\ldots,Y_m$ having common
probability
density $f$ and, respectively, $g$ are issued from the
same
population. The null hypothesis $f=g$ is opposed to a
large
nonparametric class of smooth alternatives $f$ and
$g$. We
consider several problems, according to the distance
between the
populations' densities: pointwise, interval-wise,
$L_2$ and
$L_\infty$ norms. We propose test procedures that
attain
parametric rates in some cases. In other problems, the
procedures
adapt automatically to the smoothnesses of the
underlying
densities. After a numerical study of these tests, we
prove their
theoretical properties in the classical minimax
approach.

**Mots Clés:** *Nonparametric test ; Homogeneity test ; Wavelet estimator ;
Minimax rates ; Adaptivity*

**Date:** 2003-12-15

**Prépublication numéro:** *PMA-871*