Abstract: A flexible nonparametric regression model is considered in which the response depends linearly on some covariates, with regression coefficients as additive functions of other covariates. Polynomial spline estimators are proposed for the unknown coefficient functions, with optimal univariate mean square convergence rate under geometric mixing condition. Consistent model selection method is also proposed based on a nonparametric Bayes Information Criterion (BIC). Simulations and data examples demonstrate that the polynomial spline estimators are computationally efficient and as accurate as existing local polynomial estimators.
Key words and phrases: AIC, Approximation space, BIC, German real GNP, knot, mean square convergence, spline approximation.