Bürmann expansion and test for additivity

We propose a Lagrange multiplier test for additivity based on the Burmann expansion of a conditional mean function. The asymptotic null distribution of the test is shown to be x-super-2, under some regularity conditions. In contrast, the Lagrange multiplier test proposed by Chen et al. (1995) is based on the Volterra expansion of the conditional mean function. We discuss some desirable advantages of the Burmann expansion over the Volterra expansion for nonlinear time series modelling. We also reported an empirical study which shows that, in terms of empirical power, the Lagrange multiplier test motivated by the Burmann expansion outperforms the test of Chen et al. (1995) for the cases for which the Lagrange multiplier test is designed. For other cases for which none of the tests is specifically designed, the empirical powers of the two tests are comparable. Finally, we illustrated the use of the Lagrange multiplier test with a blowfly experimental system. Copyright Biometrika Trust 2003, Oxford University Press.