Related papers: Bridging centrality and extremity: Refining empiri…
Extremile (Daouia, Gijbels and Stupfler,2019) is a novel and coherent measure of risk, determined by weighted expectations rather than tail probabilities. It finds application in risk management, and, in contrast to quantiles, it fulfills…
Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
Data depth proves successful in the analysis of multivariate data sets, in particular deriving an overall center and assigning ranks to the observed units. Two key features are: the directions of the ordering, from the center towards the…
The extremogram, proposed by Davis and Mikosch (2008), is a useful tool for measuring extremal dependence and checking model adequacy in a time series. We define the extremogram in the spatial domain when the data is observed on a lattice…
From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious.…
Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used…
Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments,…
I propose a new procedure to estimate the False Alarm Probability, the measure of significance for peaks of periodograms. The key element of the new procedure is the use of generalized extreme-value distributions, the limiting distribution…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…
In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an…