A Nonparametric Least-Squares Test for Checking a Polynomial Relationship

In this paper the interest is in testing whether a regression function is polynomial of a certain degree. One possible approach to this testing problem is to do a parametric polynomial fit and a nonparametric fit and to reject the null hypothesis of a polynomial function if the distance between the two fits if too large. Another approach consists of looking at the residuals from the parametric fit. In this paper we propose an entirely new approach to deal with the testing problem