Estimates of low bias for the multivariate normal

Christopher S. Withers (1) , Saralees Nadarajah (2)

1 Applied Mathematics Group
2 University of Manchester [Manchester]

Given a sample from a multivariate normal with mean , 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 are given with bias , where is the sample size. Simulation studies show superior performance of these estimates versus traditional ones.

Mots clés: primary; secondary; Bias reduction; Moments; Multivariate Hermite polynomials; Multivariate normal; Ratio estimates; Unbiased estimates; Wishart distribution

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Christopher S. Withers, Saralees Nadarajah. Estimates of low bias for the multivariate normal. Statistics and Probability Letters, 2011, 81 (11), pp.1635. ⟨10.1016/j.spl.2011.06.014⟩. ⟨hal-00789863⟩