This paper discusses the problem of classifying an observed stretch
X=(
x1, …,
xr) into
Π1 or
Π2, where
Πi is a Gaussian stationary process with zero mean and spectral density
fθi(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 θ
2 is contiguous to θ
1, 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.
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