Related papers: Information estimation using nonparametric copulas
In the field of finance, insurance, and system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are…
We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they…
This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…
In multivariate analysis, uncertainty arises from two sources: the marginal distributions of the variables and their dependence structure. Quantifying the dependence structure is crucial, as it provides valuable insights into the…
We propose a copula density estimator that can include information on bivariate marginals when the information is available. We use B-splines for copula density approximation and include information on bivariate marginals via a penalty…
The study of dependence between random variables is the core of theoretical and applied statistics. Static and dynamic copula models are useful for describing the dependence structure, which is fully encrypted in the copula probability…
When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
Nonparametric and machine learning methods are flexible methods for obtaining accurate predictions. Nowadays, data sets with a large number of predictors and complex structures are fairly common. In the presence of item nonresponse,…
In this paper we focus on the estimation of mutual information from finite samples $(\mathcal{X}\times\mathcal{Y})$. The main concern with estimations of mutual information is their robustness under the class of transformations for which it…
Estimating Mutual Information (MI), a key measure of dependence of random quantities without specific modelling assumptions, is a challenging problem in high dimensions. We propose a novel mutual information estimator based on parametrizing…
Data from spectrophotometers form vectors of a large number of exploitable variables. Building quantitative models using these variables most often requires using a smaller set of variables than the initial one. Indeed, a too large number…
We propose a novel estimator of the mutual information between two ordinal vectors $x$ and $y$. Our approach is inductive (as opposed to deductive) in that it depends on the data generating distribution solely through some nonparametric…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
The identification of relevant features, i.e., the driving variables that determine a process or the properties of a system, is an essential part of the analysis of data sets with a large number of variables. A mathematical rigorous…
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We present a new non-parametric estimator of the conditional density of the kernel type. It is based on an efficient transformation of the data by quantile transform. By use of the copula representation, it turns out to have a remarkable…
When facing multivariate covariates, general semiparametric regression techniques come at hand to propose flexible models that are unexposed to the curse of dimensionality. In this work a semiparametric copula-based estimator for…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…