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This paper presents an algorithm for the simulation of Hawkes-type processes where the intensity is expressed in terms of a continuous-time autoregressive moving average model. We identify upper bounds for both the univariate and the multivariate intensity functions that are used to develop simulation algorithms based on the thinning technique.

Spatially distributed functional data are prevalent in many statistical applications such as meteorology, energy forecasting, census data, disease mapping, and neurological studies. Given their complex and high-dimensional nature, functional data often require dimension reduction methods to extract meaningful information. Inverse regression is one such approach that has become very popular in the past two decades. We study the inverse regression in the framework of functional data observed at irregularly positioned spatial sites. The functional predictor is the sum of a spatially dependent functional effect and a spatially independent functional nugget effect, while the relation between the scalar response and the functional predictor is modeled using the inverse regression framework. For estimation, we consider local linear smoothing with a general weighting scheme, which includes as special cases the schemes under which equal weights are assigned to each observation or to each subject. This framework enables us to present the asymptotic results for different types of sampling plans over time such as non-dense, dense, and ultra-dense. We discuss the domain-expanding infill (DEI) framework for spatial asymptotics, which is a mix of the traditional expanding domain and infill frameworks. The DEI framework overcomes the limitations of traditional spatial asymptotics in the existing literature. Under this unified framework, we develop asymptotic theory and identify conditions that are necessary for the estimated eigen-directions to achieve optimal rates of convergence. Our asymptotic results include pointwise and $L_2$ convergence rates. Simulation studies using synthetic data and an application to a real-world dataset confirm the effectiveness of our methods.

Handling multiplicity without losing much power has been a persistent challenge in various fields that often face the necessity of managing numerous statistical tests simultaneously. Recently, $p$-value combination methods based on heavy-tailed distributions, such as a Cauchy distribution, have received much attention for their ability to handle multiplicity without the prescribed knowledge of the dependence structure. This paper delves into these types of $p$-value combinations through the lens of extreme value theory. Distributions with regularly varying tails, a subclass of heavy tail distributions, are found to be useful in constructing such $p$-value combinations. Three $p$-value combination statistics (sum, max cumulative sum, and max) are introduced, of which left tail probabilities are shown to be approximately uniform when the global null is true. The primary objective of this paper is to bridge the gap between current developments in $p$-value combination methods and the literature on extreme value theory, while also offering guidance on selecting the calibrator and its associated parameters.

This paper presents the results of the first application of BERTopic, a state-of-the-art topic modeling technique, to short text written in a morphologi-cally rich language. We applied BERTopic with three multilingual embed-ding models on two levels of text preprocessing (partial and full) to evalu-ate its performance on partially preprocessed short text in Serbian. We also compared it to LDA and NMF on fully preprocessed text. The experiments were conducted on a dataset of tweets expressing hesitancy toward COVID-19 vaccination. Our results show that with adequate parameter setting, BERTopic can yield informative topics even when applied to partially pre-processed short text. When the same parameters are applied in both prepro-cessing scenarios, the performance drop on partially preprocessed text is minimal. Compared to LDA and NMF, judging by the keywords, BERTopic offers more informative topics and gives novel insights when the number of topics is not limited. The findings of this paper can be significant for re-searchers working with other morphologically rich low-resource languages and short text.

This paper develops a general asymptotic theory of series ridge estimators for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can generate irregularly spaced sampling sites in a flexible manner including both pure increasing and mixed increasing domain frameworks. Specifically, we consider a spatial trend regression model and a nonparametric regression model with spatially dependent covariates. For these models, we investigate the $L^2$-penalized series estimation of the trend and regression functions and establish (i) uniform and $L^2$ convergence rates and (ii) multivariate central limit theorems for general series estimators, (iii) optimal uniform and $L^2$ convergence rates for spline and wavelet series estimators, and (iv) show that our dependence structure conditions on the underlying spatial processes cover a wide class of random fields including L\'evy-driven continuous autoregressive and moving average random fields.

This paper introduces several depths for random sets with possibly non-convex realisations, proposes ways to estimate the depths based on the samples and compares them with existing ones. The depths are further applied for the comparison between two samples of random sets using a visual method of DD-plots and statistical testing. The advantage of this approach is identifying sets within the sample that are responsible for rejecting the null hypothesis of equality in distribution and providing clues on differences between distributions. The method is justified using a simulation study and applied to real data consisting of histological images of mastopathy and mammary cancer tissue.

This paper aims first to perform robust continuous analysis of a mixed nonlinear formulation for stress-assisted diffusion of a solute that interacts with an elastic material, and second to propose and analyse a virtual element formulation of the model problem. The two-way coupling mechanisms between the Herrmann formulation for linear elasticity and the reaction-diffusion equation (written in mixed form) consist of diffusion-induced active stress and stress-dependent diffusion. The two sub-problems are analysed using the extended Babu\v{s}ka--Brezzi--Braess theory for perturbed saddle-point problems. The well-posedness of the nonlinearly coupled system is established using a Banach fixed-point strategy under the smallness assumption on data. The virtual element formulations for the uncoupled sub-problems are proven uniquely solvable by a fixed-point argument in conjunction with appropriate projection operators. We derive the a priori error estimates, and test the accuracy and performance of the proposed method through computational simulations.

This paper develops a flexible and computationally efficient multivariate volatility model, which allows for dynamic conditional correlations and volatility spillover effects among financial assets. The new model has desirable properties such as identifiability and computational tractability for many assets. A sufficient condition of the strict stationarity is derived for the new process. Two quasi-maximum likelihood estimation methods are proposed for the new model with and without low-rank constraints on the coefficient matrices respectively, and the asymptotic properties for both estimators are established. Moreover, a Bayesian information criterion with selection consistency is developed for order selection, and the testing for volatility spillover effects is carefully discussed. The finite sample performance of the proposed methods is evaluated in simulation studies for small and moderate dimensions. The usefulness of the new model and its inference tools is illustrated by two empirical examples for 5 stock markets and 17 industry portfolios, respectively.

We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds. Additionally, it features a highly parallel iterative scheme. To verify its efficacy, we conduct numerical experiments on some $4$-dimensional manifolds without and with boundary.

Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of the governing Richards' equation. Iterative methods are therefore required to manage the complexity of the flow problem. Norms of successive corrections in the iterative procedure form sequences of positive numbers. Definitions of computational orders of convergence and theoretical results for abstract convergent sequences can thus be used to evaluate and compare different iterative methods. We analyze in this frame Newton's and $L$-scheme methods for an implicit finite element method (FEM) and the $L$-scheme for an explicit finite difference method (FDM). We also investigate the effect of the Anderson Acceleration (AA) on both the implicit and the explicit $L$-schemes. Considering a two-dimensional test problem, we found that the AA halves the number of iterations and renders the convergence of the FEM scheme two times faster. As for the FDM approach, AA does not reduce the number of iterations and even increases the computational effort. Instead, being explicit, the FDM $L$-scheme without AA is faster and as accurate as the FEM $L$-scheme with AA.