Second order asymptotics for score tests in exponential family nonlinear models

Abstract

This paper focuses on second order asymptotic theory for score tests in exponential family nonlinear models.It gives closed-form expressions for the coefficients that define the Edgeworth expanison for the null distribution of the score test statistic when the dispersion is unknown. These coefficients can also be used to Bartlett-correct the score statistic. The results in this paper generalise a number of recent results.Simulation results show that finite-sample corrections from second order asymptotic theory can be useful to obtain tests with reliable size behaviour.An empirical application to a well known data set is also considered.

Keywords:

• Asymptotic expansion
• Bartlett-type correction
• chi-squared distribution
• Cornish-Fisher expansion
• Edgeworth expansion
• exponential family
• generalised linear models
• nonlinear models
• score test