Testing for Stochastic Order in Interval-Valued Data

TL;DR

This paper introduces a new statistical test for assessing stochastic order between two samples of interval-valued data, utilizing a U-statistic-based test statistic and comparing its performance with existing methods through real and simulated data.

Contribution

It develops a novel U-statistic-based test for stochastic order in interval data and evaluates its effectiveness against existing methods.

Findings

The proposed test performs favorably compared to the bivariate Kolmogorov-Smirnov test.

The test statistic's asymptotic distribution is derived under the null hypothesis.

Simulation and real data analyses demonstrate the method's practical utility.

Abstract

We construct a procedure to test the stochastic order of two samples of interval-valued data. We propose a test statistic which belongs to U-statistic and derive its asymptotic distribution under the null hypothesis. We compare the performance of the newly proposed method with the existing one-sided bivariate Kolmogorov-Smirnov test using real data and simulated data.