## Abstract

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.

Original language | English |
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Pages (from-to) | 1017-1026 |

Number of pages | 10 |

Journal | Journal of the American Statistical Association |

Volume | 89 |

Issue number | 427 |

DOIs | |

State | Published - 1 Jan 1994 |

## Keywords

- Bootstrap
- Censored data
- Crossing points
- Q-Q plots
- Shift function
- Treatment effect
- Two-sample problems