The asymptotic distribution of the suprema of the standardized empirical processes under the Koziol–Green model

✍ Scribed by J.K. Ghorai; J. Schmitter

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 180 KB
• Volume: 41
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00166-7

✦ Synopsis

Let ŜX (t) denote the m.l.e. of the survival function SX (t) based on the right censored data (Z1; 1); : : : ; (Zn; n) and the proportional hazards model of random censorship. The asymptotic distribution of certain linear combinations of the supremum of the standardized process { √ n( ŜX (t) -SX (t)): t ¿ 0} is shown to be an extreme value distribution. This limiting distribution is used to construct asymptotically exact conÿdence bands for the survival function SX over the entire range of the observations. These bands are found to be narrower at both ends of the survival function when compared to the bands obtained by Hollander and Peña. If the proportion of uncensored data, n, is greater than 1 2 , the bands narrow to zero width at both ends of the survival function. The bands are illustrated using simulated as well as real life data sets.