Moments and root-mean-square error of the Bayesian MMSE estimator of classification error in the Gaussian model
The Bayesian Minimum Mean-Square-Error (BMMSE) error estimator of LDA is studied. The first, second, and cross moments of the BMMSE estimator with true error are considered. Both conditional and unconditional performance metrics are analyzed. For the first time, the Kolmogorov double-asymptotic is used in a Bayesian setting. Asymptotically exact finite-sample approximations of performance metrics are derived.
performance metrics linear discriminant analysis bayesian minimum mean-square error estimator double asymptotics kolmogorov asymptotics rms