Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion

To estimate a sample quantile’s variance, the quantile spacing method involves smoothing parameter m . When m , n → ∞ , the corresponding Studentized test statistic is asymptotically N ( 0 , 1 ) . Holding m fixed instead, the asymptotic distribution contains the Edgeworth expansion term capturing the variance of the quantile spacing. Consequently, the fixed- m distribution is more accurate than the standard normal under both asymptotic frameworks. A testing-optimal m is proposed to maximize power subject to size control. In simulations, the new method controls size better than similar methods while maintaining good power. Throughout are results for two-sample quantile treatment effect inference. Code is available online.