Tests of Independence in Parametric Models with Applications and Illustrations.

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.