BOOTSTRAP CHOICE OF SMOOTHING PARAMETER OF LOCALLY WEIGHTED LINEAR REGRESSION

We consider a model y_i = g(x_i) +ε_i where x_i is an independent variable and ε_i's are iid random error with mean 0 and variance σ^2. If the regression function g(x) is smooth enough, then we may have an approximation g(x) = g(x_0)+g'(x_0)(x-x_0) for ∣ x-x_0 ∣ <___- 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) = α_x+β_xx 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.