A. Colin Cameron and Pravin K. Trivedi
"Tests of Independence in Parametric Models with Applications and Illustrations"
Journal of Business and Economic Statistics, January 1993, Vol. 11(1), pp.29-43.
Tests of independence between variables in discrete and continuous bivariate
and multivariate regression equations are derived using series expansions
of joint distributions in terms of marginal distributions and their related
orthonormal polynomials. Th e tests are conditional moment tests based on
covariances between pair s of orthonormal polynomials. Examples include tests
of serial independence against bilinear and/or autoregressive conditional
heteroskedasticity alternatives, dependence in multivariate normal regression
models, and dependence in count data models. Monte Carlo simulations based
on bivariate counts are used to evaluate the tests. A multivariate count data
model for Australian health-care utilization data is used for illustration.