Related papers: Outlier detection and a tail-adjusted boxplot base…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…

Outlier detection is a significant area in data mining. It can be either used to pre-process the data prior to an analysis or post the processing phase (before visualization) depending on the effectiveness of the outlier and its importance.…

We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…

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…

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…

Weighted Outlier Detection is a method for identifying unusual or anomalous data points in a dataset, which can be caused by various factors like human error, fraud, or equipment malfunctions. Detecting outliers can reveal vital information…

Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…

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…

A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…

We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…

Despite recent advancements in out-of-distribution (OOD) detection, most current studies assume a class-balanced in-distribution training dataset, which is rarely the case in real-world scenarios. This paper addresses the challenging task…

Outlier detection refers to the identification of anomalous samples that deviate significantly from the distribution of normal data and has been extensively studied and used in a variety of practical tasks. However, most unsupervised…

This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…

Often the challenge associated with tasks like fraud and spam detection[1] is the lack of all likely patterns needed to train suitable supervised learning models. In order to overcome this limitation, such tasks are attempted as outlier or…

Extreme quantile treatment effects (eQTEs) measure the causal impact of a treatment on the tails of an outcome distribution and are central for studying rare, high-impact events. Standard QTE methods often fail in extreme regimes due to…

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…

A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.

We propose a new outlier detection method for multi-dimensional data. The method detects outliers based on vector cosine similarity, using a new dataset constructed by adding a dimension with zero values to the original data. When a point…