Robust Bootstrap Of Nonparametric Regression Function

Bootstrap is to emulate through a certain quantity to get the statistic of interest (for example mean and standard deviation) under particular zero as-sumptionses of emulational distribution,then construct the confidence interval of the statistic and judge the statistic from the process.Bootstrap become more and more important in the modern statistical inference.Along with the increase of uncertainty,the fluctuate of data become greater, and the data will usually include singular data. For the data with outliers, Bootstrap samples may contain more "pollution" than original samples and reduce the validity of our statistical deduction. In this paper, we discuss how to use the influence function to find the probability of resampling in the non-parametric regression of the N-W estimate. We use tilting Bootstrap method (the sample probability is unequal) to obtain curve fitting, which is resistant to the presence of outliers on the regression function.