LALOË , Thomas

International audience

Let (X, Y) be a random pair taking values in H × R, where H is an infinite dimensional separable Hilbert space. We establish weak consistency of a nearest neighbor-type estimator of the regression function of Y on X based on independent observations of the pair (X, Y). As a general strategy, we propose to reduce the infinite dimension of H by...

In this paper we propose a simple new algorithm to perform clustering, based on the Alter algorithm proposed in [5] but lowering signicantly the algorithmic complexity with respect to the number of clusters. An empirical study states the relevance of our iterative process and a confrontation on simulated multivariate and functional data shows...

Using quantization techniques, Laloë (2010) defined a new clustering algorithm called Alter. This L1- based algorithm is shown to be convergent but suffers two major flaws. The number of clusters, K, must be supplied by the user and the computational cost is high. This article adapts the X-means algorithm (Pelleg & Moore, 2000) to solve both problems

Let $(X,Y)$ be a random pair taking values in ${\R^d}\times J$, where $J\subset\R$ is supposed to be bounded. We propose a plug-in estimator of the level sets of the regression function $r$ of $Y$ on $X$, using a kernel estimator of $r$. We consider an error criterion defined by the volume of the symmetrical difference between the real and...

Asymptotic normality of density estimates often requires the continuity of the underlying density and assumptions on its derivatives. Recently, these assumptions have been weakened for some estimates using the less restrictive notion of regularity index. However, the particular definition of this index makes it unusable for many estimates. In...

The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons. The first introduced method is based on binned coincidence count (Grün, 1996) and can be applied on two or more simultaneously recorded neurons. Among the...

Using quantization techniques, Laloë (2009) defined a new algorithm called Alter. This $L^1$-based algorithm is proved to be convergent, but suffers two shortcomings. First, the number of clusters $K$ has to be supplied by the user. Second, it has high complexity. In this article, we adapt the idea of $X$-means algorithm (Pelleg and Moore;...

This paper deals with the problem of estimating the level sets $L(c)= \{F(x) \geq c \}$, with $c \in (0,1)$, of an unknown distribution function $F$ on \mathbb{R}^d_+$. A plug-in approach is followed. That is, given a consistent estimator $F_n$ of $F$, we estimate $L(c)$ by $L_n(c)= \{F_n(x) \geq c \}$. We state consistency results with respect...

An important problem in risk theory is to understand the behavior of an expected cost Y ∈ R associated to d ≥ 1 risk factors which are heterogeneous in nature. We proposed in a recent work [1], a depth-based Covariate-Conditional-Tail-Expectation (CCTE) in order to quantify a loss knowing that a given risk scenario occurred: considering the...

We deal with the problem of nonparametric estimation of a multivariate regression function without any assumption on the compacity of the support of the random design, thanks to a " warping " device. An adaptive warped kernel estimator is first defined in the case of known design distribution and proved to be optimal in the oracle sense. Then,...

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate, belonging to an infinite-dimensional space. By using the first order optimality condition, we interpret these...

The asymptotic behavior of a plug-in kernel estimator of the regression level sets is studied. The exact asymtotic rate in terms of the symmetric difference is derived for a given level. Then, we exhibit the exact asymptotic rate when the level corresponds to a fixed probability and is therefore unknown.

We deal with the problem of nonparametric estimation of a multivariate regression function without any assumption on the compacity of the support of the random design. To tackle the problem, we propose to extend a "warping" device to the multivariate framework. An adaptive warped kernel estimator is first defined in the case of known design...

The aim of this paper is to study the asymptotic behavior of a particular multivariate risk measure, the Covariate-Conditional-Tail-Expectation (CCTE), based on a multivariate statistical depth function. Depth functions have become increasingly powerful tools in nonparametric inference for multivariate data, as they measure a degree of...

In this paper, we present a new functional depth called Principal Component functional Depth (PCD) for square-integrable processes X over a compact set. This depth involves a generic multivariate depth function which is evaluated at the projection of the function on the basis formed by the first J vectors of the Karhunen-Loève decomposition of...

Erratum to: Metrika DOI 10.1007/s00184-014-0498-4

The aim of this paper is to study the behavior of a covariate func-tion in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the c-upper level sets L(c) = {F (x) ≥ c}, with c ∈ (0, 1), of an unknown distribution function F on R d + . A plug-in approach is followed. We state consistency results with...

Active acoustic detection and characterization in three dimensions (3D) with multibeam sonars is a powerful technique for ecological studies of schooling fish. The alpine Lake Annecy provides ideal conditions for sampling fish with active acoustic methods: it has calm water, low species diversity, and the density of pelagic fish schools is...

The task of simplifying the complex spatio-temporal variables associated with climate modeling is of utmost importance and comes with significant challenges. In this research, our primary objective is to tailor clustering techniques to handle compound extreme events within gridded climate data across Europe. Specifically, we intend to identify...

The modeling of dependence between maxima is an important subject in several applications in risk analysis. To this aim, the extreme value copula function, characterised via the madogram, can be used as a margin-free description of the dependence structure. From a practical point of view, the family of extreme value distributions is very rich...

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with...

International audience