Goodness-of-fit Test Using Sample Quantiles

Summary A goodness-of-fit test is constructed using sample quantiles for a p.d.f. F(x, θ) (where θ is to be estimated) which is continuous and strictly increasing at the quantiles of interest. It is shown to be asymptotically equivalent, under alternatives “close” to the null, to the usual goodness-of-fit test based on grouped observations, the advantage being that we may avoid the difficulties of choosing cell boundaries for grouping.