Random weighting estimation of confidence intervals for quantiles

This paper presents a new random weighting method for confidence interval estimation for the sample -quantile. A theory is established to extend ordinary random weighting estimation from a non-smoothed function to a smoothed function, such as a kernel function. Based on this theory, a confidence interval is derived using the concept of backward critical points. The resultant confidence interval has the same length as that derived by ordinary random weighting estimation, but is distribution-free, and thus it is much more suitable for practical applications. Simulation results demonstrate that the proposed random weighting method has higher accuracy than the Bootstrap method for confidence interval estimation.