Power Loss for Inhomogeneous Poisson Processes

TL;DR

This paper analyzes the power loss of the score test compared to the Neyman-Pearson test for inhomogeneous Poisson processes with unknown parameters, using third order asymptotic properties.

Contribution

It provides a detailed asymptotic analysis of the power loss of the score test in the context of inhomogeneous Poisson processes with unknown intensity functions.

Findings

Derived the power loss formula under regularity conditions

Compared the performance of score and Neyman-Pearson tests

Quantified second and third order asymptotic properties

Abstract

In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real unknown parameter, we consider a simple hypothesis against a sequence of close (contiguous) alternatives. Under certain regularity conditions we obtain the power loss of the score test with respect to the Neyman-Pearson test. The power loss measures the performance of a second order efficient test by the help of third order asymptotic properties of the problem under consideration.