Approximate power of score test for variance heterogeneity under local alternatives in nonlinear models

Lin and Wei [2003. Testing for heteroscedasticity in nonlinear regression models. Comm. Statist. Theory Methods 32, 171–192] developed the score test for heteroscedasticity in nonlinear regression models and investigated the power of this test through Monte Carlo simulations. The main purpose of this paper is to present an approach for estimating the local power for the score test, based on a noncentral χ2χ2 approximation to such power under contiguous alternatives. The approach is also extended to nonlinear models with AR(1) errors. The methods are applied to the problem of local power calculations for the score tests of heteroscedasticity in European rabbit data [Ratkowsky, 1983. Nonlinear Regression Modelling. Marcel Dekker, New York, pp. 108–110]. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.