The Annals of Statistics

Mean residual life processes

Miklós Csörgő and Ričardas Zitikis

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Abstract

Yang and Hall and Wellner initiated investigations of the asymptotic uniform behaviour of mean residual life (MRL) processes. They obtained results holding true over fixed and expanding compact subintervals of $[0, \infty)$.

In this exposition we study MRL processes over the whole positive half-line $[0, \infty)$. We describe classes of weight functions which enable us to establish the (a) strong uniform-over-$[0, \infty)$ consistency and (b)weak uniform-over-$[0, \infty)$ approximation of MRL processes. We give examples which show the necessity of employing weight functions in order to have (a) and (b), and prove the optimality of the weight function classes which we make use of. Extending our results concerning (b), we discuss constructions of asymptotic confidence bands for unknown MRL functions. The width of the obtained confidence bands is regulated by weight functions depending on the available information on the underlying distribution function.

Article information

Source
Ann. Statist., Volume 24, Number 4 (1996), 1717-1739.

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032298292

Digital Object Identifier
doi:10.1214/aos/1032298292

Mathematical Reviews number (MathSciNet)
MR1416657

Zentralblatt MATH identifier
0933.62106

Subjects
Primary: 62N05: Reliability and life testing [See also 90B25] 62G15: Tolerance and confidence regions
Secondary: 62F17 62E20: Asymptotic distribution theory

Keywords
Mean residual life life expectancy strong consistency weak approximations confidence bands weighted empirical processes Brownian motion Brownian bridge

Citation

Csörgő, Miklós; Zitikis, Ričardas. Mean residual life processes. Ann. Statist. 24 (1996), no. 4, 1717--1739. doi:10.1214/aos/1032298292. https://projecteuclid.org/euclid.aos/1032298292


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