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We develop a constructive process which determines all extreme points of the unit ball of the space of $m$--linear forms, $m\geq1.$ Our method provides a full characterization of the geometry of that space through finitely many elementary…
Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new,…
In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…
We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme"…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of…
We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the…
Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape…
There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…
This paper proposes a method for identifying an initial gap in piecewise-linear systems from data. Piecewise-linear systems appear in many engineered systems such as degraded mechanical systems and infrastructures, and are known to show…
In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of…
The covXtreme software provides functionality for estimation of marginal and conditional extreme value models, non-stationary with respect to covariates, and environmental design contours. Generalised Pareto (GP) marginal models of peaks…
As a useful and elegant tool of extreme value theory, the study of point processes on a metric space is important and necessary for the analyses of heavy-tailed functional data. This paper focuses on the definition and properties of such…
We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms…