高维正态概率积分的降维算法与L_1逼近

高维正态概率积分计算一直是统计学家关注的课题．早期工作已由Gupta（1963）1]评价，并给出大量的参考文献．近期工作则可参考Tong（1990）2]的专著．虽然有关的文献很多，但是除了二、三维问题已有较好的算法外（例如见Zhana－Yana，19933]），更高维问题尚无公认的有效算法．在维数m＞3的高维情形，多数文章常假设积分域或相关阵有特殊形式，否则只有使用MonteCarlo方法［4］或拟MonteCarlo方法（亦称数论网格方法，例如见Fang－Wang，19945]）．但即使是被认为较好的拟MonteCarlo方法，其收敛阶仅为O（n－2／m），因此对于真…

DIMENSION REDUCTION AND L_1 APPROXIMATION FOR EVALUATION OF MULTIVARIATE NORMAL INTEGRAL

In the present paper, the authors suggest an algorithm to evaluate the multivariate normal integrals under the supposition that the correlation matrix R is quasi-decomposable, in which we have rij = aiaj for most i, j, and rij = aiaj + bij for the others, where bij's are the nonzero deviations. The algorithm makes the high-dimensional normal distribution reduce to a 2-dimensional or 3-dimensional integral which can be evaluated by the numerical method with a high precision.Our supposition is close to what we encounter in practice. When correlation matrix is arbitrary, we suggest an approximate algorithm with a medium precision, it is, in general, better than some approximate algorithms. The simulation results of about 20000 high-dimensional integrals showed that the present algorithms were very efficient.