Abstract

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.

摘要

由于大型数据集的聚合，直方图值数据越来越频繁地出现。支持许多方法（尤其是回归和主成分分析）的一项统计数据是协方差函数。迄今为止，还没有直接从边缘直方图观测值计算这些函数的方法。本文开发了通过 copula 函数来开发多元直方图值数据的参数分布的技术。特别是，提出了最大似然、边缘推断函数和规范最大似然估计方法。数值研究有助于确定哪些联结函数最适合在各种情况下使用，从而计算协方差。结果应用于真实数据集。