Related papers: Nonsymmetric Dependence Measures: the Discrete Cas…
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
In this paper, we study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
Dependent data underlies many statistical studies in the social and health sciences, which often involve sensitive or private information. Differential privacy (DP) and in particular \textit{user-level} DP provide a natural formalization of…
Asymptotic properties of a dimension-robust dependence measure are investigated. It is related to those used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to…
We study conditional independence under infinite measures on punctured product spaces, a notion recently introduced for graphical modeling in multivariate extremes and L\'evy processes. In contrast to classical probabilistic conditional…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with…
A {\em maximal inequality} seeks to estimate $\mathbb{E}\max_i X_i$ in terms of properties of the $X_i$. When the latter are independent, the union bound (in its various guises) can yield tight upper bounds. If, however, the $X_i$ are…
A semiparametric copula-based two-part quantile regression framework is developed for the analysis of semicontinuous outcomes characterized by a point mass at zero and a continuous positive component. The proposed approach models the…
Copula-based dependence modeling often relies on parametric formulations. This is mathematically convenient, but can be statistically inefficient when the parametric families are not suitable for the data and model in focus. A Bayesian…
Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured…
This paper explores the dependence modeling of financial assets in a dynamic way and its critical role in measuring risk. Two new methods, called Accelerated Moving Window method and Bottom-up method are proposed to detect the change of…
Normal copula with a correlation coefficient between $-1$ and $1$ is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H\"usler and…
We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the…
One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…
Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…