Karine Tribouley

A Wavelet Method for Confidence Intervals in the Density Model

We present a wavelet procedure for defining confidence intervals for f(x 0 ), where x 0 is a given point and f is an unknown density from which there are independent observations. We use an undersmoothing method which is shown to be near optimal (up to a logarithmic term) in a first order sense. We propose a second order correction using the Edgeworth expansion. The adaptation with respect to the unknown regularity of f is given via a Lepskii type algorithm and has the advantage to be well located. The theoretical results are proved under weak assumptions and concern very irregular or oscillating functions. An empirical study gives some hints for choosing the constant of the threshold level. The results are very encouraging for the length of the intervals as well as for the coverage accuracy. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..

Evolutionary Pareto distributions

Abstract We consider here i.i.d. variables which are distributed according to a Pareto P (α) up to some point x1 and a Pareto P (β) (with a different parameter) after this point. This model constitutes an approximation for estimating extreme tail probabilities, especially for financial or insurance data. We estimate the parameters by maximizing the likelihood of the sample, and investigate the rates of convergence and the asymptotic laws. We find here a problem which is very close to the change point question from the point of view of limits of experiments. Especially, the rates of convergence and the limiting law obtained here are the same as in a change point framework. Simulations are giving an illustration of the quality of the procedure.

SPARSE APPROXIMATION AND FIT OF INTRADAY LOAD CURVES IN A HIGH DIMENSIONAL FRAMEWORK

An important perspective in electric consumption obviously is the forecasting. A crucial step in the forecasting process is the modeling. It is commonly admitted that many variables are influential for the prediction in this context. On the other hand, a prediction, to be robust and efficient, has necessarily to rely on a small number of well chosen predictors. We are typically in a situation where sparse multidimensional modeling can bring an essential input, and this paper is an attempt to prove it. In this perspective, we shall address the question of providing a sparse representation of the intraday load curves, with good approximation properties. One difficulty is that we have here a large set of potential predictors among climate variables and shape patterns, and even if high dimensional sparse methods have clearly as objective to select among a large number of covariates, they are especially efficient when the predictors are not too correlated. So our task is twofold: first we need to operate a p...

Functional approach for excess mass estimation in the density model

We consider a multivariate density model where we estimate the excess mass of the unknown probability density

Adaptive confidence interval for pointwise curve estimation

f

Estimating copula densities through wavelets

at a given level

Nonparametric homogeneity tests

nu>0

Learning out of leaders

from

A test of goodness-of-fit for the copula densities

n

Adaptive simultaneous confidence intervals in non-parametric estimation

i.i.d. observed random variables. This problem has several applications such as multimodality testing, density contour clustering, anomaly detection, classification and so on. For the first time in the literature we estimate the excess mass as an integrated functional of the unknown density