Pointwise Interval Estimation of the Regression Function for Fix-Designed Nonparametric Regression Model

In this paper, the pointwise confidence interval and bias-corrected confidence interval are developed based on kernel estimation. Considering that the bandwidth plays an important role in kernel estimation and interval estimation, an iterative method is proposed to select proper bandwidth in estimation. The estimated intervals are proven to be asymptotically accurate and their satisfying performace are shown by simulation results.