Comparing Two Contaminated Samples

TL;DR

This paper introduces a new statistical test for comparing two contaminated samples, accounting for additive noise with known moments, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It proposes a novel polynomial-moment-based test for contaminated data, with an automatic selection method for the polynomial degree, improving comparison accuracy.

Findings

The test effectively distinguishes distributions in simulated discrete and continuous cases.

The method performs well in real-data example, demonstrating practical applicability.

Simulation results show good power against various alternatives.

Abstract

We consider the problem of testing whether two samples of contaminated data, possibly paired, are from the same distribution. Is is assumed that the contaminations are additive noises with known moments of all orders. The test statistic is based on the polynomials moments of the difference between observations and noises. . A data driven selection is proposed to choose automatically the number of involved polynomials. We present a simulation study in order to investigate the power of the proposed test within discrete and continuous cases. A real-data example is presented to demonstrate the method.