NONLOCAL BEHAVIOR IN POLYNOMIAL REGRESSIONS

Polynomial regression is a common technique for estimating conditional mean functions of unknown form. Increasing the order of the polynomia l increases the flexibility of the estimated function. This note shows with an example how these estimated polynomials, even (perhaps especi ally) higher-order ones, display undesirable nonlocal effects. That is , values of the response corresponding to a particular value or range of the predictor may have a large and undesirable influence on the pre dicted response at a very different value of the predictor.