Karine Bertin

Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data

The kernel method is a nonparametric procedure used to estimate densities with support in R. When nonnegative data are modeled, the classical kernel density estimator presents a bias problem in the neighborhood of zero. Several methods have been developed to reduce this bias, which include the boundary kernel, data transformation and reflection methods. An alternative proposal is to use kernel estimators based on distributions with nonnegative support, as is the case of the Birnbaum-Saunders (BS), gamma, inverse Gaussian and lognormal models. Generalized BS (GBS) distributions have received considerable attention, due to their properties and their flexibility in modeling different types of data. In this paper, we propose, characterize and implement the kernel method based on GBS distributions to estimate densities with nonnegative support. In addition, we provide a simple method to choose the corresponding bandwidth. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing financial real data.

Adaptive Dantzig density estimation

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candes and Taos approach, we propose an

Maximum likelihood estimators and random walks in long memory models

\ell_1

Adaptive pointwise estimation of conditional density function

-minimization under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global coherence assumptions, oracle inequalities are derived. These theoretical results are also proved to be valid for the natural Lasso estimate associated with our Dantzig procedure. Then, the issue of calibrating these procedures is studied from both theoretical and practical points of view. Finally, a numerical study shows the significant improvement obtained by our procedures when compared with other classical procedures.

LASSO-type estimators for semiparametric nonlinear mixed-effects models estimation

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum-likelihood estimators for the drift parameter. Our approach is based on the non-Gaussian case on the approximation by random walks of the driving noise. We study the asymptotic behaviour of the estimators and we give some numerical simulations to illustrate our results.

Asymptotic normality of the Nadaraya–Watson estimator for nonstationary functional data and applications to telecommunications

In this paper we consider the problem of estimating

Semi-parametric segmentation of multiple series using a DP-Lasso strategy

f

Drift parameter estimation in fractional diffusions driven by perturbed random walks

, the conditional density of

Maxiset in sup-norm for kernel estimators

Y

Adaptive estimation of conditional density function

given