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The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often…
Traditional methods for covariate adjustment of treatment means in designed experiments are inherently conditional on the observed covariate values. In order to develop a coherent general methodology for analysis of covariance, we propose a…
The passivity index, a quantitative measure of a system's passivity deficiency or excess, has been widely used in stability analysis and control. Existing studies mostly rely on scalar forms of indices, which are restrictive for…
We develop the relative Morse index theory for linear self-adjoint operator equation without compactness assumption and give the relationship between the index defined in [44] and [45]. Then we generalize the method of saddle point…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
Background: Although the missing covariate indicator method (MCIM) has been shown to be biased under extreme conditions, the degree and determinants of bias have not been formally assessed. We derived the formula for the relative bias in…
This paper introduces an econometric framework for analyzing cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the…
We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…
The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…
An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are…
In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
A new family of matrix variate distributions indexed by elliptical models are proposed in this work. The so called \emph{multimatricvariate distributions} emerge as a generalization of the bimatrix variate distributions based on matrix…