摘要：This paper discusses the problem of classifying an observed stretch X =( x 1, …, xr ) into Π 1 or Π 2, where Πi is a Gaussian stationary process with zero mean and spectral density f θi (λ). We propose a new discriminant statistic based on some estimator θ=θ( X ) of a spectral parameter. The statistic D [θ, W ] is motivated by a spectral measure with divergence function W . Most of the work presented is devoted to higher order asymptotic theory when θ2 is contiguous to θ1, in order to study the asymptotic difference between different D [θ, W ]. In particular, it is shown that for any choice of W , D [θ, W ] has the same second order averaged risk as the optimal likelihood ratio (LR) if θ belongs to an appropriate class of asymptotically efficient estimators, and the third order term of the averaged risk is minimized by the (bias-adjusted) maximum likelihood estimator (MLE). We also examine the case of the rule based on the MLE without bias adjustment.
