Estimation and testing for varying coefficients in additive models with marginal integration

We propose marginal integration estimation and testing methods for the coefficients of varying-coefficient multivariate regression models. Asymptotic distribution theory is developed for the estimation method, which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is established. These theoretical results are derived under the fairly general conditions of absolute regularity (beta-mixing). Application of the test procedure to West German real GNP (gross national product) data reveals that a partially linear varying coefficient model is best parsimonious in fitting the data dynamics, a fact that is also confirmed with residual diagnostics.