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In traditional extreme value analysis, the bulk of the data is ignored, and only the tails of the distribution are used for inference. Extreme observations are specified as values that exceed a threshold or as maximum values over distinct…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…
Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size,…
In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of…
We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between…
We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between…
In this note we discuss the mathematical tools to define trend indicators which are used to describe market trends. We explain the relation between averages and moving averages on the one hand and the so called exponential moving average…
We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification…
We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…
We propose a simple way of testing whether a given set of observations can come from a given theoretical cumulative distribution. In the test more weight is attached to the tails of the distribution than in the usual Kolmogorov or Smirnov…
Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…
We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, going back to Nagaev's seminal work. Many extensions in the…
In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation ($CTE$) for a loss distribution with a finite mean but infinite variance. The present work introduces a new…
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…
This paper presents a novel semiparametric method to study the effects of extreme events on binary outcomes and subsequently forecast future outcomes. Our approach, based on Bayes' theorem and regularly varying (RV) functions, facilitates a…
This article studies tail behavior for the error components in the stochastic frontier model, where one component has bounded support on one side, and the other has unbounded support on both sides. Under weak assumptions on the error…
The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…
Upper exponential inequalities for the tail probabilities of the centered and normalized number of triangles in the Erd\"{o}s-R\'{e}nyi graph are obtained, where the probability of every edge is fixed. The result is formulated in terms of…