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Bootstrap clustering for graph partitioning

Philippe Gambette, Alain Guénoche (2011)

RAIRO - Operations Research - Recherche Opérationnelle

Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this profile,...

Bootstrap clustering for graph partitioning∗

Philippe Gambette, Alain Guénoche (2012)

RAIRO - Operations Research

Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this profile,...

Bootstrap in nonstationary autoregression

Zuzana Prášková (2002)

Kybernetika

The first-order autoregression model with heteroskedastic innovations is considered and it is shown that the classical bootstrap procedure based on estimated residuals fails for the least-squares estimator of the autoregression coefficient. A different procedure called wild bootstrap, respectively its modification is considered and its consistency in the strong sense is established under very mild moment conditions.

Bootstrap method for central and intermediate order statistics under power normalization

Haroon Mohamed Barakat, E. M. Nigm, O. M. Khaled (2015)

Kybernetika

It has been known for a long time that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In this paper, we show that the same is true if we use the bootstrap for estimating a central, or an intermediate quantile under power normalization. A simulation study illustrates and corroborates theoretical results.

Bootstrapping the shorth for regression

Cécile Durot, Karelle Thiébot (2006)

ESAIM: Probability and Statistics

The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in...

Bound on extended f -divergences for a variety of classes

Pietro Cerone, Sever Silvestru Dragomir, Ferdinand Österreicher (2004)

Kybernetika

The concept of f -divergences was introduced by Csiszár in 1963 as measures of the ‘hardness’ of a testing problem depending on a convex real valued function f on the interval [ 0 , ∞ ) . The choice of this parameter f can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of f -divergences are given and the class of χ α -divergences is presented. Ostrowski’s inequality and a Trapezoid inequality are utilized in order to prove bounds for an extension...

Bounded solutions for ARMA model with varying coefficients

A. Makagon, A. Weron, A. Wyłomańska (2004)

Applicationes Mathematicae

The paper deals with ARMA systems of equations with varying coefficients. A complete description of bounded solutions to ARMA(1,q) systems is obtained and their uniqueness is studied. Some special cases are discussed, including the case of significant interest of systems with periodic coefficients. The paper generalizes results of [9] and opens a new direction of study.

Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process

Jean-Marc Azaïs, Christine Cierco-Ayrolles, Alain Croquette (2010)

ESAIM: Probability and Statistics

This paper uses the Rice method [18] to give bounds to the distribution of the maximum of a smooth stationary Gaussian process. We give simpler expressions of the first two terms of the Rice series [3,13] for the distribution of the maximum. Our main contribution is a simpler form of the second factorial moment of the number of upcrossings which is in some sense a generalization of Steinberg et al.'s formula ([7] p. 212). Then, we present a numerical application and asymptotic expansions...

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