Approximations to Multivariate Normal Rectangle Probabilities Based on Conditional Expectations
提出了两种基于条件期望和二元变量回归的多元正态矩形概率新近似方法，一种一阶近似快速但精度较低，另一种二阶近似更精确但计算更耗时；还针对象限概率提出了基于截断多元正态矩生成函数的第三种近似，精度介于前两者之间。这些方法在参数估计中优于已有近似和Genz数值方法。
Abstract Two new approximations for multivariate normal probabilities for rectangular regions, based on conditional expectations and regression with binary variables, are proposed. One is a second-order approximation that is much more accurate but also more numerically time-consuming than the first-order approximation. A third approximation, based on the moment-generating function of a truncated multivariate normal distribution, is proposed for orthant probabilities only. Its accuracy is between the first- and second-order approximations when the dimension is less than seven and the correlations are not large. All of the approximations get worse as correlations get larger. These new approximations offer substantial improvements on previous approximations. They also compare favorably with the methods of Genz for numerical evaluation of the multivariate normal integral. The approximation methods should be especially useful within a quasi-Newton routine for parameter estimation in discrete models that involve the multivariate normal distribution.