Bootstrap and Smoothing: Confidence Intervals for Population Quantiles

Abstract

The seminal work by Efron (1979) has laid down the landmark of a new branch of modern statistical analysis, namely bootstrap. Since then, the methods of bootstrap and smoothing have become important and practical methods in contemporary statistical analysis. Bootstrap provides a systematic way to estimate the standard errors of estimators based on resampling techniques while smoothing concerns the use of kernel function to smooth the density estimators. In this talk, I shall first provide a brief introduction to the concepts of bootstrap and smoothing, and their roles in statistical estimation and analysis. Then, I shall discuss an important research area in bootstrap and smoothing, namely the estimation of the confidence intervals for population quantiles.