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Clustering of extreme values: estimation and application
The extreme value theory (EVT) encompasses a set of methods that allow inferring about the risk inherent to various phenomena in the scope of...
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Estimating Sample Skewness from Sample Data Summaries and Associated Evaluation of Normality
AbstractWe propose a method to estimate a sample skewness from the given summary statistics and give explicit formulas for the most common scenarios....
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Estimating the Extremal Coefficient: A Simulation Comparison of Methods
Tail dependence is an important issue to evaluate risk. The multivariate extreme values theory is the most suitable to deal with the extremal...
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A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model
In this manuscript, we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy...
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Convolution and Risk Class Aggregation
The chapter shows how to use convolution to estimate the overall loss distribution and the Value-at-Risk of each risk class. To take into account the...
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New Exploratory Tools for Extremal Dependence: \(\chi \) Networks and Annual Extremal Networks
Understanding dependence structure among extreme values plays an important role in risk assessment in environmental studies. In this work, we propose...
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A Graphical Tool for Copula Selection Based on Tail Dependence
In many practical applications, the selection of copulas with a specific tail behaviour may allow to estimate properly the region of the distribution...
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Automatic Clustering for Seasonal Time Series Based on Entropy
Automatic clustering for seasonal time series based on entropy is a tool developed to understand decision-making behaviours for economic agents. An...
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Identifying groups of variables with the potential of being large simultaneously
Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate...
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A tuning-free efficient test for marginal linear effects in high-dimensional quantile regression
This work is concerned with testing the marginal linear effects of high-dimensional predictors in quantile regression. We introduce a novel test that...
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Copula Models and Diagnostics for Multivariate Interval-Censored Data
In studies concerning disease progression or patient survival, multivariate time-to-event outcomes are increasingly used as endpoints. The exact...
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Conjunction of a Flood and a Storm
The case study in this chapter involves the conjunction of two climate hazards: a flood (high river flow) and a storm (strong wind), which we label...
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Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool
A flexible model called the max-mixture model has been introduced for modeling situations where the extremal dependence structure type may vary with...
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Spatial extremes and stochastic geometry for Gaussian-based peaks-over-threshold processes
Geometric properties of exceedance regions above a given quantile level provide meaningful theoretical and statistical characterizations for...
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Power M-Estimators for Location and Scatter
Power M-estimators for location and scatter are studied by Frahm et al. (J. Multivariate Anal. 176:104569, 2020) in the context of missing data. It...
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Multivariate Extreme Value Theory: Practice and Limits
This chapter presents the most recent developments in extreme value theory in cases of joint, or multivariate, hazards. This type of phenomenon is...
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Introduction
An essential component of a basic introductory statistics course is describing classic methods for making inferences about a population of...
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From Normality to Skewed Multivariate Distributions: A Personal View
An overview of the development of multivariate distributions’ theory is given starting with T. W. Anderson’s monograph [1]. In the book, multivariate...
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Rank Correlation
This chapter discusses the rank correlation and its extensions. The rank vector is introduced in section 1. This is followed by a discussion of...