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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....

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 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 estimations of non-negative random variables distributions

František Vávra, Pavel Nový, Hana Mašková, Michala Kotlíková, David Zmrhal (2003)

Kybernetika

The problem of estimation of distribution functions or fractiles of non- negative random variables often occurs in the tasks of risk evaluation. There are many parametric models, however sometimes we need to know also some information about the shape and the type of the distribution. Unfortunately, classical approaches based on kernel approximations with a symmetric kernel do not give any guarantee of non-negativity for the low number of observations. In this note a heuristic approach, based on...

Nonparametric regression estimation based on spatially inhomogeneous data: minimax global convergence rates and adaptivity

Anestis Antoniadis, Marianna Pensky, Theofanis Sapatinas (2014)

ESAIM: Probability and Statistics

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known density g with a finite number of well-separated zeros. In particular, we consider two different cases: when g has zeros of a polynomial order and when g has zeros of an exponential order. These two cases correspond to moderate and severe data losses, respectively. We obtain asymptotic (as the sample size increases)...

Note on universal algorithms for learning theory

Karol Dziedziul, Barbara Wolnik (2007)

Applicationes Mathematicae

We study the universal estimator for the regression problem in learning theory considered by Binev et al. This new approach allows us to improve their results.

Notes on the evolution of feature selection methodology

Petr Somol, Jana Novovičová, Pavel Pudil (2007)

Kybernetika

The paper gives an overview of feature selection techniques in statistical pattern recognition with particular emphasis on methods developed within the Institute of Information Theory and Automation research team throughout recent years. Besides discussing the advances in methodology since times of Perez’s pioneering work the paper attempts to put the methods into a taxonomical framework. The methods discussed include the latest variants of the optimal algorithms, enhanced sub-optimal techniques...

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