The Annals of Statistics

Large Sample Estimates and Uniform Confidence Bounds for the Failure Rate Function Based on a Naive Estimator

J. Sethuraman and Nozer D. Singpurwalla

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Abstract

In this paper we consider a naive estimator of the failure rate function and smooth it using any band-limited window. We show that this smoothed estimate is equivalent to estimates obtainable from the sample hazard function, as in Rice and Rosenblatt (1976). We obtain the asymptotic distribution of the global deviation of the smoothed estimate from the failure rate function, which can then be used to construct uniform confidence bands.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 628-632.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345466

Digital Object Identifier
doi:10.1214/aos/1176345466

Mathematical Reviews number (MathSciNet)
MR615438

Zentralblatt MATH identifier
0484.62058

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G15: Gaussian processes 62G05: Estimation 62N05: Reliability and life testing [See also 90B25]

Keywords
Failure rate function consistent estimate asymptotic uniform confidence bands maxima of stationary processes

Citation

Sethuraman, J.; Singpurwalla, Nozer D. Large Sample Estimates and Uniform Confidence Bounds for the Failure Rate Function Based on a Naive Estimator. Ann. Statist. 9 (1981), no. 3, 628--632. doi:10.1214/aos/1176345466. https://projecteuclid.org/euclid.aos/1176345466


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