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Time series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However,…

Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…

Computer Vision and Pattern Recognition · Computer Science 2018-04-16 Cheng-Hao Deng , Wan-Lei Zhao

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…

Statistics Theory · Mathematics 2021-08-20 Nathawut Phandoidaen , Stefan Richter

In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper…

Statistics Theory · Mathematics 2008-12-23 Christian Y. Robert , Johan Segers , Christopher A. T. Ferro

In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…

Methodology · Statistics 2011-06-28 Elvira Romano , Antonio Balzanella , Rosanna Verde

Policy-makers are often faced with the task of distributing a limited supply of resources. To support decision-making in these settings, statisticians are confronted with two challenges: estimands are defined by allocation strategies that…

Methodology · Statistics 2024-04-01 Aaron L. Sarvet , Julien D. Laurendeau , Mats J. Stensrud

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

Optimization and Control · Mathematics 2018-09-05 S. Borgwardt , F. Happach

This paper studies limit measures of stationary measures of stochastic ordinary differential equations on the Euclidean space and tries to determine which invariant measures of an unperturbed system will survive. Under the assumption for…

Dynamical Systems · Mathematics 2022-01-28 Tianyuan Xu , Lifeng Chen , Jifa Jiang

Goulden and Jackson introduced a very powerful method to study the distributions of certain consecutive patterns in permutations, words, and other combinatorial objects which is now called the cluster method. There are a number of natural…

Combinatorics · Mathematics 2017-06-06 Ran Pan , Jeffrey Brian Remmel

Following the works of Berthet (1997), we first obtain exact clustering rates in the functional law of the iterated logarithm for the uniform empirical and quantile processes and for their increments. In a second time, we obtain functional…

Statistics Theory · Mathematics 2012-01-27 Davit Varron

The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…

Statistics Theory · Mathematics 2013-03-27 Richard A. Davis , Thomas Mikosch , Yuwei Zhao

The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…

Statistical Mechanics · Physics 2017-10-10 Yong Zhu , Xiaosong Chen

The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, the maxima are taken over disjoint blocks of observations.…

Statistics Theory · Mathematics 2018-02-28 Axel Bücher , Johan Segers

We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space $D(0,\infty)$.…

Probability · Mathematics 2020-03-12 Zaoli Chen , Gennady Samorodnitsky

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

Probability · Mathematics 2009-11-11 V. Shcherbakov

In this article, we consider a sequence $(N_n)_{n \geq 1}$ of point processes, whose points lie in a subset $E$ of $\bR \verb2\2 \{0\}$, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient…

Probability · Mathematics 2010-11-17 Raluca Balan , Sana Louhichi

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than {\epsilon} ({\epsilon} > 0). It is known ([BM05]) that the empirical measure of these fragments converges in law, under some…

Probability · Mathematics 2022-10-17 Camille Noûs , Sylvain Rubenthaler

We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise…

Probability · Mathematics 2025-09-09 Sergey Berezin

Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…

Data Structures and Algorithms · Computer Science 2011-02-16 Filippo Utro

We present a new algorithm for clustering longitudinal data. Data of this type can be conceptualized as consisting of individuals and, for each such individual, observations of a time-dependent variable made at various times. Generically,…

Machine Learning · Computer Science 2026-03-17 Marie-Pierre Sylvestre , Laurence Boulanger