Related papers: Large deviation inequalities for sums of indicator…
It was shown that when one disposes of a parametric information of the truncation distribution, the semiparametric estimator of the distribution function for truncated data (Wang, 1989) is more efficient than the nonparametric one. On the…
We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.
We present order of magnitude estimates for the quantiles of non-negative linear combinations of non-negative random variables, as well as deviation inequalities for general linear combinations of independent random variables, under the…
This paper is the Part II of a serious work about T product tensors focusing at establishing new probability bounds for sums of random, independent, T product tensors. These probability bounds characterize large deviation behavior of the…
Consider an expander graph in which a $\mu$ fraction of the vertices are marked. A random walk starts at a uniform vertex and at each step continues to a random neighbor. Gillman showed in 1993 that the number of marked vertices seen in a…
Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…
We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for…
We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…
Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the…
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probability tail. Aban, Meerschaert and Panorska (2006) derived the…
The Markov, Chebyshev, and Chernoff inequalities are some of the most widely used methods for bounding the tail probabilities of random variables. In all three cases, the bounds are tight in the sense that there exists easy examples where…
This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
Let X_1,..., X_n be independent Bernoulli random variables and $f$ a function on {0,1}^n. In the well-known paper (Talagrand1994) Talagrand gave an upper bound for the variance of f in terms of the individual influences of the X_i's. This…