On Local Polynomial Smoothers and Their Competitors
نویسنده
چکیده
Local polynomial smoothers recently received much attention in the literature, owing to their optimality properties (Fan, 1993). However, Seifert and Gasser (1996a; 1996b) showed that in finite samples these smoothers may suffer problems arising from data sparseness. To overcome this problem they suggest a modification based on ridge regression ideas. In this paper we shall describe another approach, based on interpolation techniques proposed by Hall and Turlach (1997b). This method is easy to implement, and simulation results show that it significantly improves the finite-sample performance of local polynomial smoothers while not interfering with their asymptotic properties. We shall also discuss how interpolation methods (and other schemes) can be used to improve the performance of other well-known smoothers. Using appropriate modifications the performance of these smoothers can be improved to the extent of being arbitrarily close to that of local polynomial smoothers.
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