Two‐sample Nonparametric Tilting Method

summary Efron introduced the one‐sample nonparametric tilting method for constructing confidence intervals. The method enjoys some good features such as being range‐respecting and having internal studentizing and good coverage accuracy. This paper presents a two‐sample version of the one‐sample non‐parametric tilting method for dealing with two independent sample problems, whereby each of the two individual samples is ‘tilted’ separately by different amounts. The paper shows that careful choice of the two tilting parameters produces second‐order accurate confidence limits. Further, saddlepoint approximations can be used to avoid extensive Monte Carlo simulations, and it turns out that the approximations are exceptionally easy to apply with the tilting parameters. Numerical examples illustrate the two‐sample nonparametric tilting method.