INFERENCE FOR SHIFT FUNCTIONS IN THE 2-SAMPLE PROBLEM WITH RIGHT-CENSORED DATA - WITH APPLICATIONS

For two distribution functions, F and G, the shift function is defined by Delta(t) = G(-1) . F(t) - t. The shift function is the distance fr om the 45 degrees line and the quantity plotted in Q-Q plots. In the a nalysis of lifetime data, Delta represents the difference between two treatments. The shift function can also be used to find crossing point s of two distribution functions. The large-sample distribution theory for estimates of Delta is studied for right-censored data. It turns ou t that the asymptotic covariance function depends on the unknown distr ibution functions F and G; hence simultaneous confidence bands cannot be directly constructed. A construction of simultaneous confidence ban ds for Delta is developed via the bootstrap. Construction and applicat ion of such bands are explored for the Q-Q plot.