On APF Test for Poisson Process with Shift and Scale Parameters

TL;DR

This paper introduces a new goodness-of-fit test for inhomogeneous Poisson processes with unknown shift and scale parameters, demonstrating that the test statistic's limit distribution is independent of these parameters under the null hypothesis.

Contribution

The paper proposes a Cramer-von Mises type test statistic for inhomogeneous Poisson processes with unknown parameters and analyzes its asymptotic properties, showing parameter independence under the null.

Findings

Limit distribution of the test statistic is parameter-free under null hypothesis

The test is applicable to inhomogeneous Poisson processes with unknown shift and scale

Asymptotic behavior of the test statistic is characterized

Abstract

We propose the goodness of fit test for inhomogeneous Poisson processes with unknown scale and shift parameters. A test statistic of Cramer-von Mises type is proposed and its asymptotic behavior is studied. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameters.