Tests of Independence in Parametric Models With Applications and Illustrations

Abstract

Tests of independence between variables in a wide variety of discrete and continuous bivariate and multivariate regression equations are derived using results from the theory of series expansions of joint distributions in terms of marginal distributions and their related orthonormal polynomials. The tests are conditional moment tests based on covariances between pairs of orthonormal polynomials. Examples include tests of serial independence against bilinear and/or autoregressive conditional heteroscedasticity alternatives, tests of dependence in multivariate normal regression models, and dependence in count-data models. Monte Carlo simulation based on bivariate count models is used to evaluate the. size and power properties of the proposed tests. A multivariate count-data model for Australian health-care-utilization data is used to empirically illustrate the tests.

KEY WORDS:

• ARCH and Bilinear Models
• Count Data
• Dynamic Information Matrix Test
• Orthogonal Polynomials
• Score test
• Series expansions