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:**

- 62G05 Estimation
- 62G20 Asymptotic properties
- 62C20 Minimax procedures

**Résumé:** We consider the problem of testing hypotheses about
the contours in binary images observed on the regular grid.
We propose a simple
goodness-of-fit test of the hypothesis that a contour
belongs to a given
parametric family against a nonparametric alternative.
We analyze the behavior of the test under the null hypothesis,
and under the alternative separated from the null parametric family
by a distance of order $n^{-1/2}$ ($n$ is the total number of
observations and the distance is defined as the measure of symmetric
difference between the sets whose boundaries are the contours
of interest). Finally, we prove the lower bound
showing that no test can be consistent if the distance
between the hypothesis and the alternative is
of the order smaller than
$n^{-1/2}$.

**Mots Clés:** *Parametric versus nonparametric hypotheses testing ; goodness-of-fit ; minimax rate of testing ; binary image model*

**Date:** 1999-06-24

**Prépublication numéro:** *PMA-512*