Moments and root-mean-square error of the Bayesian MMSE estimator of classification error in the Gaussian model

作者:

Highlights:

• 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.

摘要

Highlights•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.

论文关键词:Linear discriminant analysis,Bayesian minimum mean-square error estimator,Double asymptotics,Kolmogorov asymptotics,Performance metrics,RMS

论文评审过程:Received 14 May 2013, Revised 27 August 2013, Accepted 23 November 2013, Available online 3 December 2013.

论文官网地址:https://doi.org/10.1016/j.patcog.2013.11.022