New weighted $L^2$-type tests for the inverse Gaussian distribution

TL;DR

This paper introduces a new weighted $L^2$-type goodness-of-fit test for the inverse Gaussian distribution, demonstrating its theoretical validity and superior finite-sample performance through simulations and real data applications.

Contribution

The paper develops a novel weighted $L^2$ test for the inverse Gaussian distribution, including asymptotic theory, bootstrap validation, and empirical performance comparison.

Findings

The new test is asymptotically valid under the null hypothesis.

It outperforms classical and recent tests in finite samples.

The test is successfully applied to real data sets.

Abstract

We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a broad class of alternative distributions. These results are used to show that the parametric bootstrap procedure, which we employ to implement the test, is asymptotically valid and that the whole test procedure is consistent. A comparative simulation study for finite sample sizes shows that the new procedure is competitive to classical and recent tests, outperforming these other methods almost uniformly over a large set of alternative distributions. The use of the newly proposed test is illustrated with two observed data sets.