Assessing the Distribution Consistency of Sequential Data

TL;DR

This paper introduces a non-parametric test for assessing whether a new batch of data maintains the same distribution as previous observations, using Edgeworth expansion to improve accuracy and address discrete data cases.

Contribution

It proposes a novel distribution consistency test based on Edgeworth expansion, applicable to both continuous and discrete data, with analysis of convergence rates.

Findings

The test effectively detects distribution changes in sequential data.

Edgeworth expansion improves the approximation accuracy.

Convergence rates vary between continuous and discrete cases.

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 Cram\`er's condition of smoothness is not satisfied. The rate of convergence for the various cases are compared.