Related papers: Nested Archimedean copulas: a new class of nonpara…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
No existing nested Archimedean copula tool handles all three of (a) arbitrary per-variable (right-)censoring in survival analysis, (b) arbitrary nesting trees, and (c) exact parameter gradients. Existing implementations handle only…
This paper introduces a robust estimation framework based solely on the copula function. We begin by introducing a family of divergence measures tailored for copulas, including the \(\alpha\)-, \(\beta\)-, and \(\gamma\)-copula divergences,…
We propose a new generative modeling technique for learning multidimensional cumulative distribution functions (CDFs) in the form of copulas. Specifically, we consider certain classes of copulas known as Archimedean and hierarchical…
We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
In a recent paper Noh et al. (2013) proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means…
Auxiliary information can increase the efficiency of survey estimators through an assisting model when the model captures some of the relationship between the auxiliary data and the study variables. Despite their superior properties,…
A new method for combining several initial estimators of the regression function is introduced. Instead of building a linear or convex optimized combination over a collection of basic estimators $r_1,\dots,r_M$, we use them as a collective…
The abundance of new cosmological data becoming available means that a wider range of cosmological models are testable than ever before. However, an important distinction must be made between parameter fitting and model selection. While…
The NPMLE of a distribution function from doubly truncated data was introduced in the seminal paper of Efron and Petrosian. The consistency of the Efron-Petrosian estimator depends however on the assumption of independent truncation. In…
Four types of explicit estimators are proposed here to estimate the loss rates of the links in a network with the tree topology and all of them are derived by the maximum likelihood principle. One of the four is developed from an estimator…
We construct the COpula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork…
In this paper, we study large losses arising from defaults of a credit portfolio. We assume that the portfolio dependence structure is modelled by the Archimedean copula family as opposed to the widely used Gaussian copula. The resulting…
Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear…
Classical estimators, the cornerstones of statistical inference, face insurmountable challenges when applied to important emerging classes of Archimedean copulas. These models exhibit pathological properties, including numerically unstable…
Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships…
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…
We describe here a new method to estimate copula measure. From N observations of two variables X and Y, we draw a huge number m of subsamples (size n<N), and we compute the joint ranks in these subsamples. Then, for each bivariate rank…
Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $\sigma$-space, a moduli space of fully…