Estimates of low bias for the multivariate normal

Given a sample from a multivariate normal with mean μ, a method is given for obtaining estimates with low bias for a function of the parameters. When the function is a product of positive powers of the parameters, an unbiased estimate is available. Estimates of ratios like μ1/μ2μ1/μ2 are given with bias ∼n−5∼n−5, where nn is the sample size. Simulation studies show superior performance of these estimates versus traditional ones.