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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 estimates and tests of independence in semiparametric copula models

Salim Bouzebda, Amor Keziou (2010)

Kybernetika

We introduce new estimates and tests of independence in copula models with unknown margins using φ -divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior or a boundary value of the parameter space. Simulation results show that the choice of χ 2 -divergence has good properties in terms of efficiency-robustness.

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...

New results on the NBUFR and NBUE classes of life distributions

E. M. Shokry, A. N. Ahmed, E. A. Rakha, H. M. Hewedi (2009)

Applicationes Mathematicae

Some properties of the "new better than used in failure rate" (NBUFR) and the "new better than used in expectation" (NBUE) classes of life distributions are given. These properties include moment inequalities and moment generating functions behaviors. In addition, nonparametric estimation and testing of the survival functions of these classes are discussed.

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....

Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming

Jean-Sébastien Roy, Arnaud Lenoir (2008)

Kybernetika

We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application...

Nonparametric bivariate estimation for successive survival times.

Carles Serrat, Guadalupe Gómez (2007)

SORT

Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for the second...

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...

Nonparametric estimation of the derivatives of the stationary density for stationary processes

Emeline Schmisser (2013)

ESAIM: Probability and Statistics

In this article, our aim is to estimate the successive derivatives of the stationary density f of a strictly stationary and β-mixing process (Xt)t≥0. This process is observed at discrete times t = 0,Δ,...,nΔ. The sampling interval Δ can be fixed or small. We use a penalized least-square approach to compute adaptive estimators. If the derivative f(j)belongs to the Besov space B 2 , ∞ α B 2 , ∞ α , then our estimator converges at rate (nΔ)−α/(2α+2j+1). Then we consider a diffusion with known diffusion coefficient....

Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes

Romain Azaïs, François Dufour, Anne Gégout-Petit (2013)

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

This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to...

Nonparametric estimation: the survival function.

Alfonso García Pérez (1984)

Trabajos de Estadística e Investigación Operativa

The unknown survival function S(t) of a random variable T ≥ 0 is considered. First we study the properties of S(t) and then, we estimate it from a Bayesian point of view. We compare the estimator with the posterior mean and we finish giving Bayes rules for linear functions of S(t).

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