Related papers: High-Dimensional Tail Index Regression
We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
With the growing popularity of online social media, identifying influential users in these social networks has become very popular. Existing works have studied user attributes, network structure and user interactions when measuring user…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Ratios of central order statistics seem to be very useful for estimating the tail of the distributions and therefore, quantiles outside the range of the data. In 1995 Isabel Fraga Alves investigated the rate of convergence of three…
We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical…
Real-world data often follows a long-tailed distribution, which makes the performance of existing classification algorithms degrade heavily. A key issue is that samples in tail categories fail to depict their intra-class diversity. Humans…
News articles are extremely time sensitive by nature. There is also intense competition among news items to propagate as widely as possible. Hence, the task of predicting the popularity of news items on the social web is both interesting…
Models of contagion dynamics, originally developed for infectious diseases, have proven relevant to the study of information, news, and political opinions in online social systems. Modelling diffusion processes and predicting viral…
One potential solution to combat the scarcity of tail observations in extreme value analysis is to integrate information from multiple datasets sharing similar tail properties, for instance, a common extreme value index. In other words, for…
A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…
We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to…
Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…
This article presents a short case study in text analysis: the scoring of Twitter posts for positive, negative, or neutral sentiment directed towards particular US politicians. The study requires selection of a sub-sample of representative…
This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…
This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…
This paper presents a method to validate the true patrons of a brand, group, artist or any other entity on the social networking site Twitter. We analyze the trend of total number of tweets, average retweets and total number of followers…