TESTING FOR VARYING DISPERSION IN EXPONENTIAL FAMILY NONLINEAR MODELS

BO-CHENG WEI^{1}, JIAN-QING SHI^{1,2}, WING-KAM FUNG^{3} AND YUE-QING HU^{1}

1Department of Mathematics, Southeast University, Nanjing 210096, China 2Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China 3Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong, China

(Received March 22, 1995; revised March 28, 1997)

Abstract. A diagnostic model and several new diagnostic statistics are proposed for testing for varying dispersion in exponential family nonlinear models. A score statistic and an adjusted score statistic based on Cox and Reid (1987, J. Roy. Statist. Soc. Ser. B, 55, 467–471) are derived in normal, inverse Gaussian, and gamma nonlinear models. An adjusted likelihood ratio statistic is also given for normal and inverse Gaussian nonlinear models. The results of simulation studies are presented , which show that the adjusted tests keep their sizes better and are more powerful than the ordinary tests.

Key words and phrases: Adjusted profile likelihood, exponential family nonlinear models, gamma model, inverse Gaussian model, score statistic, simulation study, varying dispersion.