Inference for Shift Functions in the Two-Sample Problem With Right-Censored Data: With Applications

• Published in: Journal of the American Statistical Association 1994-09, Vol.89 (427), p.1017-1026
• Main Authors: Lu, Henry H. S., Wells, Martin T., Tiwari, Ram C.
• Format: Article
• Language: English
• Subjects: Bootstrap; Bootstrap resampling; Censored data; Censorship; Contour lines; Covariance; Crossing points; Distribution functions; Estimators; Exact sciences and technology; Inference; Mathematics; Nonparametric inference; Probability and statistics; Q-Q plots; Sampling distributions; Sciences and techniques of general use; Shift function; Statistics; Theory and Methods; Treatment effect; Two-sample problems; Uniforms
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.1994.10476837

For two distribution functions, F and G, the shift function is defined by Δ(t) = G −1 · F(t) - t. The shift function is the distance from the 45° line and the quantity plotted in Q-Q plots. In the analysis of lifetime data, A represents the difference between two treatments. The shift function can also be used to find crossing points of two distribution functions. The large-sample distribution theory for estimates of Δ is studied for right-censored data. It turns out that the asymptotic covariance function depends on the unknown distribution functions F and G; hence simultaneous confidence bands cannot be directly constructed. A construction of simultaneous confidence bands for Δ is developed via the bootstrap. Construction and application of such bands are explored for the Q-Q plot.