Curve fitting by polynomial-trigonometric regression

Abstract

We consider a method of estimating an unknown regression curve by regression on a combination of low-order polynomial terms and trigonometric terms. Estimation based on trigonometric functions alone is known to suffer from bias problems at the boundaries due to the periodic nature of the fitted functions. We show that these boundary problems are alleviated by adding low-order polynomial terms. The utility of the method is illustrated with examples, and asymptotic results show that the estimators are competitive with other nonparametric procedures. Applications to estimation in semiparametric models are also considered with particular emphasis on the case of analysis of covariance when the relationship between the response and the covariate is difficult to model parametrically.