Related papers: Functional Extreme-PLS
In traditional multivariate data analysis, dimension reduction and regression have been treated as distinct endeavors. Established techniques such as principal component regression (PCR) and partial least squares (PLS) regression…
Since the extreme value index (EVI) controls the tail behaviour of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent developments in the estimation of EVI along with covariates have…
In this paper, we estimate the sparse dependence structure in the tail region of a multivariate random vector, potentially of high dimension. The tail dependence is modeled via a graphical model for extremes embedded in the H\"usler-Reiss…
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
The modelling of multivariate extreme events is important in a wide variety of applications, including flood risk analysis, metocean engineering and financial modelling. A wide variety of statistical techniques have been proposed in the…
Partial Least Squares (PLS) refer to a class of dimension-reduction techniques aiming at the identification of two sets of components with maximal covariance, to model the relationship between two sets of observed variables…
In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension reduction problems. First, we provide a concentration…
This paper introduces the partial Gini covariance, a novel dependence measure that addresses the challenges of high-dimensional inference with heavy-tailed errors, often encountered in fields like finance, insurance, climate, and biology.…
In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…
We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest.…
Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…