The Annals of Statistics

Mean residual life processes

Miklós Csörgő and Ričardas Zitikis

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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

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

First available in Project Euclid: 17 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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