使用 Bernstein Yett-均匀先验的贝叶斯 Copula 密度估计

使用 Bernstein 多项式检验二元 Copula 的对称性

Testing Symmetry for Bivariate Copulas using Bernstein Polynomials

提出基于经验 Bernstein copula 过程的二元 copula 对称性检验，构造三个统计量并给出乘子自助实现，模拟和实际数据均验证其优越且稳定。

Variational Gaussian Copula Inference

We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and automated variational Gaussian copula approach, in which the parametric Gaussian copula family is able to preserve multivariate posterior dependence, and the nonparametric transformations based on Bernstein polynomials provide ample flexibility in characterizing the univariate marginal posteriors.

基于平滑棋盘Bernstein筛的条件Copula非参数估计

Nonparametric Estimation of Conditional Copula using Smoothed Checkerboard Bernstein Sieves

针对条件copula半参数估计需选择参数模型的问题，提出基于经验棋盘Bernstein copula的全非参数估计方法，推导了条件依赖度量的闭式估计，证明了大样本相合性，并通过模拟和实际案例验证了其性能。

Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulas

In this paper we review Bernstein and grid-type copulas for arbitrary dimensions and general grid resolutions in connection with discrete random vectors possessing uniform margins. We further suggest a pragmatic way to fit the dependence structure of multivariate data to Bernstein copulas via grid-type copulas and empirical contingency tables. Finally, we discuss a Monte Carlo study for the simulation and PML estimation for aggregate dependent losses form observed windstorm and flooding data.

Nonparametric estimation of multivariate copula using empirical bayes method

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 easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are non-smooth and often not genuine copula making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator but the estimation of tuning parameters remains elusive. In this paper, by u…

Cumulative Conditional Expectation Index

In this paper we study the cumulative conditional expectation function (CCEF) in the copula context. It is shown how to compute CCEF in terms of the cumulative copula function, this natural representation allows to deduce some useful properties, for instance with applications to convex combination of copulas. We introduce approximations of CCEF based on Bernstein polynomial copulas. We introduce estimators for CCEF, which were constructed through Bernstein polynomial estimators for copulas. The estimators are asymptotically normal and biased for CCEF.