抄録
We consider a model yi=g(xi)+εi where xi is an independent variable and εi's are iid random error with mean 0 and variance σ2. If the regression function g(x) is smooth enough, then we may have an approximation g(x)=g(x0)+g'(x0)(x-x0) for |x-x0|≤h where h is small enough. Thus, at a given point x in the range of the independent variable, a locally weighted linear regression estimate g(x)=αx+βxx sounds very reasonable. However, performance of the estimate depends on h that determines the amount of smoothing. In this article, a bootstrap method is applied for the choice of the smoothing parameter and also for some distributional problems. Simulation study is carried out for various regression functions.
