Related papers: High-Dimensional Tail Index Regression

Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. 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…

The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…

We propose a robust estimator for the tail index of Pareto-type distributions under random right-censoring, constructed within the minimum density power divergence (MDPD) framework and based on the Nelson--Aalen estimator of the cumulative…

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…

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

Aggregated data in real world recommender applications often feature fat-tailed distributions of the number of times individual items have been rated or favored. We propose a model to simulate such data. The model is mainly based on social…

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…

The massive diffusion of online social media allows for the rapid and uncontrolled spreading of conspiracy theories, hoaxes, unsubstantiated claims, and false news. Such an impressive amount of misinformation can influence policy…

Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…

The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…

Recently, Twitter has become the social network of choice for sharing and spreading information to a multitude of users through posts called 'tweets'. Users can easily re-share these posts to other users through 'retweets', which allow…

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…

We introduce an original mathematical model to analyse the diffusion of posts within a generic online social platform. The main novelty is that each user is not simply considered as a node on the social graph, but is further equipped with…

Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…

There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.

We propose a multivariate generative model to capture the complex dependence structure often encountered in business and financial data. Our model features heterogeneous and asymmetric tail dependence between all pairs of individual…

A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…

The importance of the ability of predict trends in social media has been growing rapidly in the past few years with the growing dominance of social media in our everyday's life. Whereas many works focus on the detection of anomalies in…