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In this paper, we begin our discussion with some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid…
(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…
On the basis of the dynamical interpretation of Monte Carlo simulations, we discuss the relation of the equilibrium relaxation time, the susceptibility and the statistical error. We introduce a new quantity called {\it the statistical…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…
Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…
In general, underestimation of risk is something which should be avoided as far as possible. Especially in financial asset management, equity risk is typically characterized by the measure of portfolio variance, or indirectly by quantities…
In recent years, probabilistic forecasting is an emerging topic, which is why there is a growing need of suitable methods for the evaluation of multivariate predictions. We analyze the sensitivity of the most common scoring rules,…
Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of…
Multi-agent imitation learning aims to train multiple agents to perform tasks from demonstrations by learning a mapping between observations and actions, which is essential for understanding physical, social, and team-play systems. However,…
Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…
We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple…
A critical task in systems biology is the identification of genes that interact to control cellular processes by transcriptional activation of a set of target genes. Many methods have been developed to use statistical correlations in…
When two variables are related by a known function, the coefficient of determination (denoted $R^2$) measures the proportion of the total variance in the observations that is explained by that function. This quantifies the strength of the…
We propose a new measure related with tail dependence in terms of correlation: quantile correlation coefficient of random variables X, Y. The quantile correlation is defined by the geometric mean of two quantile regression slopes of X on Y…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
By deriving influence functions related to multiple-set linear canonical analysis (MSLCA) we show that the classical version of this analysis, based on empirical covariance operators, is not robust. Then, we introduce a robust version of…