Bandwidth Selector For Double-smoothing Local Linear Ression

In this paper,firstly, we introduce several nonparametric methods for estimating the mean regression function using local polynomial regression fitting, especially,local linear regression(LL) and double smoothing local linear(DSLL).The goal of this ar-ticle is to develop a effective bandwidth selector for double smoothing local linear.A constant bandwidth is not flexible enough for estimating curves with a complicat-ed shape. Because of the consideration lead to introducing a variable bandwidth h/a(·), where α(·)is some nonnegative function reflecting the variable amount of smoothing at each data point. We will study the double smoothing local linear with variable bandwidth. The proposed method combines the ideas of local linear smoothes double smoothing local linear and variable bandwidth. so it also inherits the advantages of both approaches. We give expressions for the asymptotic condi-tional mean integrated squared error(AMISE) of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Simulations illustrate the proposed estimation method.we only discus the interior points.