Rényi confidence bands (Q2714394)

Let \(F_n(x)\) be the empirical distribution of a random sample of size \(n\), where the sample elements have distribution function \(F(x)\). \textit{A. Rényi} [Acta Math. Acad. Sci. Hung. 4, 191-231 (1953; Zbl 0052.14202)] has determined the asymptotic distributions of NEWLINE\[NEWLINE\sup_{F(x)\leq 1-p}(F_n(x)-F(x))/(1-F(x))NEWLINE\]NEWLINE and related statistics. Based on these asymptotic distributions and their extensions, confidence bands are given for both the distribution and the survival functions, the width of which at each point is proportional to the estimator of the function to be estimated. Certain combinations of these bands are also proposed. An English version of this paper can be found in Stud. Sci. Math. Hung. 34, No.1-3, 71-87 (1998; Zbl 0905.62050).