Copulas and Histogram-Valued Data
针对直方图值数据，提出通过连接函数构建多元参数分布的方法，包括三种估计技术，用于计算协方差函数，并通过数值研究指导连接函数选择。
Histogram-valued data are emerging increasingly often as a consequence of the aggregation of large datasets. One statistic that underpins many methodologies especially regression and principal component analyses is the covariance function. To date, no method exists for calculating these functions directly from the marginal histogram observations. This article develops techniques through copula functions to develop a parametric distribution for multivariate histogram-valued data. In particular, maximum likelihood, inference function for margins, and canonical maximum likelihood estimation methods are proposed. A numerical study helps to ascertain which copulas are best to use in various cases, and thence to calculate the covariances. The results are applied to a real dataset.