Range of correlation matrices for dependent Bernoulli random variables
相依伯努利随机变量相关矩阵的可行范围
We say that a pair (p, R) is compatible if there exists a multivariate binary distribution with mean vector p and correlation matrix R. In this paper we study necessary and sufficient conditions for compatibility for structured and unstructured correlation matrices. We give examples of correlation matrices that are incompatible with any p. Using our results we show that the parametric binary models of Emrich & Piedmonte (1991) and Qaqish (2003) allow a good range of…