Related papers: Asymptotic theory for extreme value generalized ad…
In many random phenomena, such as life-testing experiments and environmental data (like rainfall data), there are often positive values and an excess of zeros, which create modeling challenges. In life testing, immediate failures result in…
Anomaly detection (AD) has attracted considerable attention in both academia and industry. Due to the lack of anomalous data in many practical cases, AD is usually solved by first modeling the normal data pattern and then determining if…
We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined…
We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined…
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…
We propose a nonparametric method for estimating the conditional quantile function that admits a generalized additive specification with an unknown link function. This model nests single-index, additive, and multiplicative quantile…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme…
Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been…
A key building block in the design of ultra-reliable communication systems is a wireless channel model that captures the statistics of rare events occurring due to significant fading. In this paper, we propose a novel methodology based on…
Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the…
Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly 2-dimensional situations. This paper contributes theoretical understanding, physically based models,…
We study four different approaches to model time-dependent extremal behavior: dynamics introduced by (a) a state-space model (SSM), (b) a shot-noise-type process with GPD marginals, (c) a copula-based autoregressive model with GPD…
We present a strategy for computing asymptotics of coefficients of $d$-variate algebraic generating functions. Using known constructions, we embed the coefficient array into an array represented by a rational generating functions in $d+1$…
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
The generalized persistence (GP) model, developed in the context of estimating ``value added'' by individual teachers to their students' current and future test scores, is one of the most flexible value-added models in the literature.…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…