Likelihood-based tests in zero-inflated power series models

ABSTRACT

We address the issue of performing testing inference in the class of zero-inflated power series models. These models provide a straightforward way of modelling count data and have been widely used in practical situations. The likelihood ratio, Wald and score statistics provide the basis for testing the parameter of inflation of zeros in this class of models. In this paper, in addition to the well-known test statistics, we also consider the recently proposed gradient statistic. We conduct Monte Carlo simulation experiments to evaluate the finite-sample performance of these tests for testing the parameter of inflation of zeros. The numerical results show that the new gradient test we propose is more reliable in finite samples than the usual likelihood ratio, Wald and score tests. An empirical application to real data is considered for illustrative purposes.

KEYWORDS:

• Excess of zeros
• large-sample tests
• likelihood-based inference
• power series distributions

Acknowledgments

We deeply thank the anonymous referees for the valuable comments and suggestions which have improved considerably the first version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Artur Lemonte gratefully acknowledges the financial support of the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) (grant 301808/2016-3).