A Type of Second-Order Asymptotic Independence
Ole Eiler Barndorff-Nielsen, P. Blæsild · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1992
SUMMARY Suppose that a random vector x is partitioned into two subvectors and that generic coordinates of these subvectors are indicated by xa, xb, … and xr, xs, … respectively. If the joint cumulant (matrix) (ka,r) equals 0 then xa and xr are asymptotically independent to order O(n -1/2) under ordinary repeated sampling. When the third-order joint cumulant (array) (ka,b,r) is also 0 this independence statement may be sharpened to asymptotic independence to order O(n -1) of xr and the residuals of xa after quadratic regression on xr. Various examples where this applies to likelihood analysis are discussed.