Asymptotic results for model robust regression
Since the mid 1980's many statisticians have studied methods for combining parametric and nonparametric models to improve the quality of fits in a regression problem. Notably Einsporn (1987) proposed the Model Robust Regression 1 estimate (MRR1) in which the parametric function, f, and the nonparametric function, g, were combined in a straightforward fashion via the use of a mixing parameter, lambda. This technique was studied extensively at small samples and was shown to be quite effective at modeling various unusual functions. In this paper we have asymptotic results for the MRR1 estimate in the case where lambda is theoretically optimal, is asymptotically optimal and data driven, and is chosen with the PRESS statistic (Allen, 1971). We demonstrate that the MRR1 estimate with lambda chosen by the PRESS statistic is slightly inferior asymptotically to the other two estimates, but, nevertheless possesses positive asymptotic qualities.
asymptotics mixing parameter semiparametric rate of convergence