相关论文: Inference for overparametrized hierarchical Archim…

Research on structure determination and parameter estimation of hierarchical Archimedean copulas (HACs) has so far mostly focused on the case in which all appearing Archimedean copulas belong to the same Archimedean family. The present work…

While there is substantial need for dependence models in higher dimensions, most existing models quickly become rather restrictive and barely balance parsimony and flexibility. Hierarchical constructions may improve on that by grouping…

One of the features inherent in nested Archimedean copulas, also called hierarchical Archimedean copulas, is their rooted tree structure. A nonparametric, rank-based method to estimate this structure is presented. The idea is to represent…

In survival analysis, subjects often face competing risks; for example, individuals with cancer may also suffer from heart disease or other illnesses, which can jointly influence the prognosis of risks and censoring. Traditional survival…

The class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of $d$-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a…

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent…

Estimation of extreme value copulas is often required in situations where available data are sparse. Parametric methods may then be the preferred approach. A possible way of defining parametric families that are simple and, at the same…

While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the…

We develop and analyze the HulC, an intuitive and general method for constructing confidence sets using the convex hull of estimates constructed from subsets of the data. Unlike classical methods which are based on estimating the (limiting)…

Explicit functional forms for the generator derivatives of well-known one-parameter Archimedean copulas are derived. These derivatives are essential for likelihood inference as they appear in the copula density, conditional distribution…

Copula-based dependence modeling often relies on parametric formulations. This is mathematically convenient, but can be statistically inefficient when the parametric families are not suitable for the data and model in focus. A Bayesian…

We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

Existing tests for factorial designs in the nonparametric case are based on hypotheses formulated in terms of distribution functions. Typical null hypotheses, however, are formulated in terms of some parameters or effect measures,…

Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…

We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…

In multiple testing, the family-wise error rate can be bounded under some conditions by the copula of the test statistics. Assuming that this copula is Archimedean, we consider two non-parametric Archimedean generator estimators. More…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…