Related papers: Tail-robust factor modelling of vector and tensor …
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the $\ell_0$-norm of the mean change vector, we separately consider dense and sparse…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
This paper deals with the dimension reduction for high-dimensional time series based on common factors. In particular we allow the dimension of time series $p$ to be as large as, or even larger than, the sample size $n$. The estimation for…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
Most factor modelling research in vector or matrix-valued time series assume all factors are pervasive/strong and leave weaker factors and their corresponding series to the noise. Weaker factors can in fact be important to a group of…
Real-world data is laden with outlying values. The challenge for machine learning is that the learner typically has no prior knowledge of whether the feedback it receives (losses, gradients, etc.) will be heavy-tailed or not. In this work,…
We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and…
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…
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…
This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order. We propose to truncate and properly dither the data prior…
This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regression (QR) models featuring conditional heteroskedasticity. I use data augmentation schemes to render the model conditionally Gaussian and…
This paper considers a structural-factor approach to modeling high-dimensional time series and space-time data by decomposing individual series into trend, seasonal, and irregular components. For ease in analyzing many time series, we…
Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…
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…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…
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…