Related papers: Continuous indetermination and average likelihood …
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…
We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals,…
Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…