© 2003 by Biometrika Trust
Bürmann expansion and test for additivity
1 Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.Akung-sik-chan{at}uiowa.edu 2 Department of Informatics, University of Oslo, N-0316 Oslo, Norway anjab{at}ifi.uio.no 3 Division of Zoology, Department of Biology, University of Oslo, P.O.Box 1050 Blindern, N-0316 Oslo, Norway n.c.stenseth{at}bio.uio.no
We propose a Lagrange multiplier test for additivity based on the Bürmann expansion of a conditional mean function.The asymptotic null distribution of the test is shown to be x2, 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 Bürmann 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 Bürmann 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.
Key Words: Alternating conditional expectations; Blowfly; Lagrange multiplier test; Nonlinear time series; Sieve; Volterra expansion
Received July 2001. Revised February 2002