Assessing the Distribution Consistency of Sequential Data

Abstract

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The keypoint is to approximate the distribution of the n+k observations by the distribution of n-k among the n observations. Edgeworth expansion gives the correcting term and the rate of convergence. We also study the discrete distribution case, for which Cramèr's condition of smoothness is not satisfied. The rate of convergence for the various cases are compared.

20 pages, 0 figures