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On estimating population characteristics from record‐breaking observations II. Nonparametric results

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  • Francisco J. Samaniego
  • Lyn R. Whitaker

Abstract

Consider an experiment in which only record‐breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X1,K1,X2,K2, …, where X1,X2, … are successive minima and K1,K2, … are the numbers of trials needed to obtain new records. Such data arise in life testing and stress testing and in industrial quality‐control experiments. When only a single sequence of random records are available, efficient estimation of the underlying distribution F is possible only in a parametric framework (see Samaniego and Whitaker [9]). In the present article we study the problem of estimating certain population quantiles nonparametrically from such data. Furthermore, under the assumption that the process of observing random records can be replicated, we derive and study the nonparametric maximum‐likelihood estimator F̂ of F. We establish the strong uniform consistency of this estimator as the number of replications grows large, and identify its asymptotic distribution theory. The performance of F̂ is compared to that of two possible competing estimators.

Suggested Citation

  • Francisco J. Samaniego & Lyn R. Whitaker, 1988. "On estimating population characteristics from record‐breaking observations II. Nonparametric results," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 221-236, April.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:2:p:221-236
    DOI: 10.1002/1520-6750(198804)35:23.0.CO;2-2
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    1. Francisco J. Samaniego & Lyn R. Whitaker, 1986. "On estimating population characteristics from record‐breaking observations. i. parametric results," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(3), pages 531-543, August.
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    Cited by:

    1. Ram C. Tiwari & Jyoti N. Zalkikar, 1991. "Bayesian inference of survival curve from record‐breaking observations: Estimation and asymptotic results," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 599-609, August.
    2. Narayanaswamy Balakrishnan & Alexei Stepanov, 2013. "Runs Based on Records: Their Distributional Properties and an Application to Testing for Dispersive Ordering," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 583-594, September.

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    1. Ram C. Tiwari & Jyoti N. Zalkikar, 1991. "Bayesian inference of survival curve from record‐breaking observations: Estimation and asymptotic results," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 599-609, August.
    2. Narayanaswamy Balakrishnan & Alexei Stepanov, 2013. "Runs Based on Records: Their Distributional Properties and an Application to Testing for Dispersive Ordering," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 583-594, September.

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