Journal of Data Science

Abstract: It is always useful to have a confidence interval, along with a single estimate of the parameter of interest. We propose a new algorithm for kernel based interval estimation of a density, with an aim to minimize the coverage error. The bandwidth used in the estimator is chosen by minimizing a bootstrap estimate of the absolute value of the coverage error. The resulting confidence interval seems to perform well, in terms of coverage accuracy and length, especially for large sample size. We illustrate our methodology with data on the eruption durations for the Old Faithful geyser in USA. It seems to be the first bandwidth selector in the literature for kernel based interval estimation of a density.