A composite quantile function estimator with applications in bootstrapping

In this note we define a composite quantile function estimator in order to improve the accuracy of the classical bootstrap procedure in small sample setting. The composite quantile function estimator employs a parametric model for modelling the tails of the distribution and uses the simple linear interpolation quantile function estimator to estimate quantiles lying between 1/(n + 1) and n/(n + 1). The method is easily programmed using standard software packages and has general applicability. It is shown that the composite quantile function estimator improves the bootstrap percentile interval coverage for a variety of statistics and is robust to misspecification of the parametric component. Moreover, it is also shown that the composite quantile function based approach surprisingly outperforms the parametric bootstrap for a variety of small sample situations.