An Exact Cholesky Decomposition and the Generalized Inverse of the Variance–Covariance Matrix of the Multinomial Distribution, with Applications
多项分布协方差矩阵的精确 Cholesky 分解、广义逆及应用
SUMMARY A symbolic formula is given for the square-root-free Cholesky decomposition of the variance–covariance matrix of the multinomial distribution. The evaluation of the symbolic Cholesky factors requires much fewer arithmetic operations than does the general Cholesky algorithm. Since the symbolic formula is not affected by an ill-conditioned matrix, it is particularly useful when the elements of a probability vector are of quite different orders of magnitude. A simpler…