42,148 research outputs found
Distribution and Dependence of Extremes in Network Sampling Processes
We explore the dependence structure in the sampled sequence of large
networks. We consider randomized algorithms to sample the nodes and study
extremal properties in any associated stationary sequence of characteristics of
interest like node degrees, number of followers or income of the nodes in
Online Social Networks etc, which satisfy two mixing conditions. Several useful
extremes of the sampled sequence like th largest value, clusters of
exceedances over a threshold, first hitting time of a large value etc are
investigated. We abstract the dependence and the statistics of extremes into a
single parameter that appears in Extreme Value Theory, called extremal index
(EI). In this work, we derive this parameter analytically and also estimate it
empirically. We propose the use of EI as a parameter to compare different
sampling procedures. As a specific example, degree correlations between
neighboring nodes are studied in detail with three prominent random walks as
sampling techniques
Modeling extreme values of processes observed at irregular time steps: Application to significant wave height
This work is motivated by the analysis of the extremal behavior of buoy and
satellite data describing wave conditions in the North Atlantic Ocean. The
available data sets consist of time series of significant wave height (Hs) with
irregular time sampling. In such a situation, the usual statistical methods for
analyzing extreme values cannot be used directly. The method proposed in this
paper is an extension of the peaks over threshold (POT) method, where the
distribution of a process above a high threshold is approximated by a
max-stable process whose parameters are estimated by maximizing a composite
likelihood function. The efficiency of the proposed method is assessed on an
extensive set of simulated data. It is shown, in particular, that the method is
able to describe the extremal behavior of several common time series models
with regular or irregular time sampling. The method is then used to analyze Hs
data in the North Atlantic Ocean. The results indicate that it is possible to
derive realistic estimates of the extremal properties of Hs from satellite
data, despite its complex space--time sampling.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS711 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes
In modeling spatial extremes, the dependence structure is classically
inferred by assuming that block maxima derive from max-stable processes.
Weather stations provide daily records rather than just block maxima. The point
process approach for univariate extreme value analysis, which uses more
historical data and is preferred by some practitioners, does not adapt easily
to the spatial setting. We propose a two-step approach with a composite
likelihood that utilizes site-wise daily records in addition to block maxima.
The procedure separates the estimation of marginal parameters and dependence
parameters into two steps. The first step estimates the marginal parameters
with an independence likelihood from the point process approach using daily
records. Given the marginal parameter estimates, the second step estimates the
dependence parameters with a pairwise likelihood using block maxima. In a
simulation study, the two-step approach was found to be more efficient than the
pairwise likelihood approach using only block maxima. The method was applied to
study the effect of El Ni\~{n}o-Southern Oscillation on extreme precipitation
in California with maximum daily winter precipitation from 35 sites over 55
years. Using site-specific generalized extreme value models, the two-step
approach led to more sites detected with the El Ni\~{n}o effect, narrower
confidence intervals for return levels and tighter confidence regions for risk
measures of jointly defined events.Comment: Published at http://dx.doi.org/10.1214/14-AOAS804 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Spatial-temporal rainfall simulation using generalized linear models
We consider the problem of simulating sequences of daily rainfall at a network of sites in such a way as to reproduce a variety of properties realistically over a range of spatial scales. The properties of interest will vary between applications but typically will include some measures of "extreme'' rainfall in addition to means, variances, proportions of wet days, and autocorrelation structure. Our approach is to fit a generalized linear model (GLM) to rain gauge data and, with appropriate incorporation of intersite dependence structure, to use the GLM to generate simulated sequences. We illustrate the methodology using a data set from southern England and show that the GLM is able to reproduce many properties at spatial scales ranging from a single site to 2000 km 2 ( the limit of the available data)
- …