Limit theorems for maxima of heavy-tailed terms with random dependent weights

We study the general case when the weights Wj , j N can be dependent and in particular long-range dependent. Under mild tail and convergence conditions on the weights Wjs, we establish limit theorems for scaled versions of the process fMn(t)gt_0, as n ! 1. The limit processes are mixtures of extremal Frechet processes. The results are valid when the laws of the Uj’s belong to the normal domain of attraction of a Frechet distribution or to a sub-class of the general domain of attraction of a Frechet law

Weak convergence to the tangent process of the linear multifractional stable motion

We also show that one can have degenerate tangent processes Z(t), when the function H(t) is not sufficiently regular. The LMSM process is closely related to the Gaussian multifractional Brownian motion (MBM) process. We establish similar weak convergence results for the MBM

Max-stable sketches: estimation of Lp-norms, dominance norms and point queries for non-negative signals

Max-stable random sketches can be computed efficiently on fast streaming positive data sets by using only sequential access to the data. They can be used to answer point and Lp-norm queries for the signal. There is an intriguing connection between the so-called p-stable (or sum-stable) and the max-stable sketches. Rigorous performance guarantees through error-probability estimates are derived and the algorithmic implementation is discussed

Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion

2000 Mathematics Subject Classification: 60G18, 60E07We also show that one can have degenerate tangent processes Z(t), when the function H(t) is not sufficiently regular. The LMSM process is closely related to the Gaussian multifractional Brownian motion (MBM) process. We establish similar weak convergence results for the MBM.This research was partially supported by the NSF Grant DMS-0102410 at Boston University

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.We study the general case when the weights Wj , j N can be dependent and in particular long-range dependent. Under mild tail and convergence conditions on the weights Wjs, we establish limit theorems for scaled versions of the process fMn(t)gt_0, as n ! 1. The limit processes are mixtures of extremal Frechet processes. The results are valid when the laws of the Uj's belong to the normal domain of attraction of a Frechet distribution or to a sub-class of the general domain of attraction of a Frechet law.This research was partially supported by a Rackham faculty research fellowship at the University of Michigan, Ann Arbor and the NSF Grant DMS-0505747 at Boston Universit

PhytoKeys at 100: progress in sustainability, innovation, and speed to enhance publication in plant systematics

The file attached is the Published/publisher’s pdf version of the article.This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.NHM Repositor

From text to structured data: Converting a word-processed floristic checklist into Darwin Core Archive format

The paper describes a pilot project to convert a conventional floristic checklist, written in a standard word processing program, into structured data in the Darwin Core Archive format. After peer-review and editorial acceptance, the final revised version of the checklist was converted into Darwin Core Archive by means of regular expressions and published thereafter in both human-readable form as traditional botanical publication and Darwin Core Archive data files. The data were published and indexed through the Global Biodiversity Information Facility (GBIF) Integrated Publishing Toolkit (IPT) and significant portions of the text of the paper were used to describe the metadata on IPT. After publication, the data will become available through the GBIF infrastructure and can be re-used on their own or collated with other data.This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.NHM Repositor

Estimating heavy-tail exponents through max self-similarity

In this paper, a novel approach to the problem of estimating the heavy-tail exponent α >; 0 of a distribution is proposed. It is based on the fact that block-maxima of size m scale at a rate m 1/α for independent, as well as for a number of dependent data. This scaling rate can be captured well by the max-spectrum plot of the data that leads to regression based estimators for α. Consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution. The proposed estimators have an important computational advantage over existing methods; namely, they can be calculated and updated sequentially in an on-line fashion without having to store the entire data set. Practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed. Extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes, robust to contaminants and continues to work under the presence of substantial amount of dependence. The proposed estimators are used to illustrate the close connection between long-range dependence and heavy tails over an Internet traffic trace.Manuscript received June 11, 2007; revised September 24, 2010; accepted September 24, 2010. Date of current version February 18, 2011. The work of S. A. Stoev and G. Michailidis was supported in part by NSF Grant DMS-0806094. The work of M. S. Taqqu was supported in part by NSF Grant DMS-0706786. (DMS-0806094 - NSF; DMS-0706786 - NSF)First author draf