Nonparametric Confidence Interval for Quantiles

Quantiles, which are also known as values-at-risk in finance, frequently arise in practice as measures of risk. Confidence interval for quantiles are typically constructed via large sample theory or the sectioning.One of the ways for achieving the confidence interval for quantiles is direct use of a central limit theorem. In this approach, we require a good estimator of the quantile density function. In this paper, we consider the nonparametric estimator of the quantile density function from Soni et al. (2012) and we obtain confidence interval for quantiles. In the following, by using simulation, the coverage probability and mean square error of this confidence interval is calculated. Also, we compare our proposed approach with alternative approaches such as sectioning and jackknife