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Local superefficiency of data-driven projection density estimators in continuous time.

Denis Bosq, Delphine Blanke (2004)

SORT

We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F0 of densities that is dense in the family of all possible densities, and a «reasonable» rate elsewhere. The class F0 may be chosen previously by the analyst. Results apply to Rd-valued processes and to N-valued processes. In the particular case where square-integrable local time does exist, it is shown that our estimator is strictly better than the local...

Mean square error of the estimator of the conditional hazard function

Abbes Rabhi, Samir Benaissa, El Hadj Hamel, Boubaker Mechab (2013)

Applicationes Mathematicae

This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.

Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies

Yuri I. Ingster, Irina A. Suslina (2010)

ESAIM: Probability and Statistics

We observe an infinitely dimensional Gaussian random vector x = ξ + v where ξ is a sequence of standard Gaussian variables and v ∈ l2 is an unknown mean. We consider the hypothesis testing problem H0 : v = 0versus alternatives H ε , τ : v ∈ V ε for the sets V ε = V ε ( τ , ρ ε ) ⊂ l 2 . The sets Vε are lq-ellipsoids of semi-axes ai = i-s R/ε with lp-ellipsoid of semi-axes bi = i-r pε/ε removed or similar Besov bodies Bq,t;s (R/ε) with Besov bodies Bp,h;r (pε/ε) removed. Here τ = ( κ , R ) or τ = ( κ , h , t , R ) ; κ = ( p , q , r , s ) are the parameters which define the sets Vε for given radii...

Nearest neighbor classification in infinite dimension

Frédéric Cérou, Arnaud Guyader (2006)

ESAIM: Probability and Statistics

Let X be a random element in a metric space (F,d), and let Y be a random variable with value 0 or 1. Y is called the class, or the label, of X. Let (Xi,Yi)1 ≤ i ≤ n be an observed i.i.d. sample having the same law as (X,Y). The problem of classification is to predict the label of a new random element X. The k-nearest neighbor classifier is the simple following rule: look at the k nearest neighbors of X in the trial sample and choose 0 or 1 for its label according to the majority vote. When ( ℱ , d ) = ( ℝ d , | | . | | ) , Stone...

New M-estimators in semi-parametric regression with errors in variables

Cristina Butucea, Marie-Luce Taupin (2008)

Annales de l'I.H.P. Probabilités et statistiques

In the regression model with errors in variables, we observe n i.i.d. copies of (Y, Z) satisfying Y=fθ0(X)+ξ and Z=X+ɛ involving independent and unobserved random variables X, ξ, ɛ plus a regression function fθ0, known up to a finite dimensional θ0. The common densities of the Xi’s and of the ξi’s are unknown, whereas the distribution of ɛ is completely known. We aim at estimating the parameter θ0 by using the observations (Y1, Z1), …, (Yn, Zn). We propose an estimation procedure based on the least...

Nonparametric adaptive estimation for pure jump Lévy processes

F. Comte, V. Genon-Catalot (2010)

Annales de l'I.H.P. Probabilités et statistiques

This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at n discrete instants with fixed sampling interval. We construct a collection of estimators obtained by deconvolution methods and deduced from appropriate estimators of the characteristic function and its first derivative. We obtain a bound for the -risk, under general assumptions on the model. Then we propose a penalty function that allows to build an adaptive estimator....

Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation

Van Hanh Nguyen, Catherine Matias (2014)

ESAIM: Probability and Statistics

In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of p-values under the null hypothesis and the other component f is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component f in the mixture, relying on a preliminary estimator of the...

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