A note on order statistics-based parametric pattern classification

• We present the OS-based classification scheme for distributions in the exponential family.
• We show that CMOS using 2-OS attains the optimal Bayesian bound for symmetric distributions.
• We compare CMOS with the existing classification paradigms for asymmetric distributions.

Recently, a novel classification paradigm is proposed, named Classification by Moments of Order Statistics (CMOS), which is shown to attain the optimal Bayesian bound for symmetric distributions and a near-optimal accuracy for asymmetric distributions [13] and [9]. However, in the process of deriving the order statistics-based classification scheme, the authors use a plausible relation “E[Φ(xk,n)]=k/(n+1)⟹E[xk,n]=Φ−1(k/(n+1))E[Φ(xk,n)]=k/(n+1)⟹E[xk,n]=Φ−1(k/(n+1))”, where ΦΦ is the cumulative distribution function of random variable XX, and xk,nxk,n is the k-th order statistics of a sample of size n from X. Therefore, the new approach actually should be viewed as the classification scheme based on the percentiles of distribution, instead of the so-called order statistics-based classification. In this paper, we will build the CMOS using 2-OS criteria in its true sense. Furthermore, we show that the order statistics-based classification reaches the optimal Bayesian bound for symmetric distributions, and compare the accuracy of CMOS, Bayesian classification, median-based classifier and percentiles-based classification for non-symmetric distributions. The theoretical results are verified by rigorous experiments as well.