Local Fitting of Regression Models by Likelihood: What's Important?
Nils Lid Hjort, M. C. Jones · NORA - Norwegian Open Research Archives · 1994
In this short essay, we look at an attractive way of performing semi parametric regression.A 'vehicle' parametric model is fit locally using kernel weights, in an extension of earlier local likelihood and local least squares polynomial fitting methods.We argue that performance is primarily affected by the number of parameters in the vehicle model for the regression mean, which determines the order of the bias.Secondly, there is also an effect of the exact form of the vehicle model: if this model is 'right' the method has the potential to behave in a fully parametric way, with its efficiency advantages, and otherwise the method should behave like a nonparametric estimator.Specifications like the right parametric form for the likelihood or perhaps just for the variance are relatively unimportant.These conclusions are based on asymptotic approximations.