Bootstrap CI and test statistics for kernel density estimates using Stata

Abstract

In recent years non-parametric density estimation has been extensively employed in several fields as a powerful descriptive tool, which is far more informative and robust than histograms. Moreover, the increased computation power of modern computers has made non-parametric density estimation a relatively "cheap" computation, helping to easily detect unexpected aspects of the distribution such as bimodality. However, it is also often neglected that non-parametric methods can only provide an estimate of the true density, whose reliability depends on various factors, such as the number of data available and the bandwidth. We will focus here on kernel density estimation and discuss the problem of computing bootstrap confidence intervals and test statistics for point-wise density estimation using Stata. Construction of confidence intervals and test of hypothesis about the true density are carried out using an asymptotically pivotal studentized statistic after computing a suitable estimator for its variance. The issue of asymptotic biased correction is also discussed and tackled.