To validate pollution data, subject-matter experts in Airpl (an organizationthat maintains a network of air pollution monitoring stations in westernFrance) daily perform visual examinations of the data and check theirconsistency. In this paper, we describe these visual examinations andpropose a formalization for this problem. The examinations consistin comparisons of so-called shorth intervals so we build a statisticaltest that compares such intervals in a nonparametric regression model.This allows to detect atypical data. A practical applicationof the test is given.

We are interested in the rate function of the moderate deviation principle for the two-sample matching problem. This is related to the determination of 1-Lipschitzfunctions with maximal variance. We give an exact solution for random variables which havenormal law, or are uniformly distributed on the Euclidean ball.

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by twoparameters. The first parameter governs the lacunarity of the waveletcoefficients while the second one governs its intensity. In this paper,we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal (in the Le Cam sense) tests on the intensity parameter.