75 research outputs found
-means clustering of extremes
The -means clustering algorithm and its variant, the spherical -means
clustering, are among the most important and popular methods in unsupervised
learning and pattern detection. In this paper, we explore how the spherical
-means algorithm can be applied in the analysis of only the extremal
observations from a data set. By making use of multivariate extreme value
analysis we show how it can be adopted to find "prototypes" of extremal
dependence and we derive a consistency result for our suggested estimator. In
the special case of max-linear models we show furthermore that our procedure
provides an alternative way of statistical inference for this class of models.
Finally, we provide data examples which show that our method is able to find
relevant patterns in extremal observations and allows us to classify extremal
events
Recommended from our members
Application of Distance Covariance to Extremes and Time Series and Inference for Linear Preferential Attachment Networks
This thesis covers four topics: i) Measuring dependence in time series through distance covariance; ii) Testing goodness-of-fit of time series models; iii) Threshold selection for multivariate heavy-tailed data; and iv) Inference for linear preferential attachment networks.
Topic i) studies a dependence measure based on characteristic functions, called distance covariance, in time series settings. Distance covariance recently gathered popularity for its ability to detect nonlinear dependence. In particular, we characterize a general family of such dependence measures and use them to measure lagged serial and cross dependence in stationary time series. Assuming strong mixing, we establish the relevant asymptotic theory for the sample auto- and cross- distance correlation functions.
Topic ii) proposes a goodness-of-fit test for general classes of time series model by applying the auto-distance covariance function (ADCV) to the fitted residuals. Under the correct model assumption, the limit distribution for the ADCV of the residuals differs from that of an i.i.d. sequence by a correction term. This adjustment has essentially the same form regardless of the model specification.
Topic iii) considers data in the multivariate regular varying setting where the radial part is asymptotically independent of the angular part as goes to infinity. The goal is to estimate the limiting distribution of given , which characterizes the tail dependence of the data. A typical strategy is to look at the angular components of the data for which the radial parts exceed some threshold. We propose an algorithm to select the threshold based on distance covariance statistics and a subsampling scheme.
Topic iv) investigates inference questions related to the linear preferential attachment model for network data. Preferential attachment is an appealing mechanism based on the intuition “the rich get richer” and produces the well-observed power-law behavior in net- works. We provide methods for fitting such a model under two data scenarios, when the network formation is given, and when only a single-time snapshot of the network is observed
Parametric and non-parametric estimation of extreme earthquake event: the joint tail inference for mainshocks and aftershocks
In an earthquake event, the combination of a strong mainshock and damaging
aftershocks is often the cause of severe structural damages and/or high death
tolls. The objective of this paper is to provide estimation for the probability
of such extreme events where the mainshock and the largest aftershocks exceed
certain thresholds. Two approaches are illustrated and compared -- a parametric
approach based on previously observed stochastic laws in earthquake data, and a
non-parametric approach based on bivariate extreme value theory. We analyze the
earthquake data from the North Anatolian Fault Zone (NAFZ) in Turkey during
1965-2018 and show that the two approaches provide unifying results
Men Are More Likely to Be Homeless Than Women
Gender has an impact on people with mental illnesses. Men are more likely to be homeless than women. More social support needs to be provided to members of both gendersYork's Knowledge Mobilization Unit provides services and funding for faculty, graduate students, and community organizations seeking to maximize the impact of academic research and expertise on public policy, social programming, and professional practice. It is supported by SSHRC and CIHR grants, and by the Office of the Vice-President Research & Innovation.
[email protected]
www.researchimpact.c
- …