The Annals of Statistics

On Testing Whether New is Better Than Used Using Randomly Censored Data

Yoshiki Kumazawa

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Under a model of random censorship, we consider the test $H_0$: a life distribution is exponential, versus $H_1$: it is new better than used, but not exponential. This paper introduces a class of tests by using the Kaplan-Meier estimator for the sample distribution in the uncensored model. Under some regularity conditions, the asymptotic normality of statistics is derived by an application of von Mises' method, and asymptotically valid tests are obtained by using estimators for the null standard deviations. The efficiency loss in the proportional censoring model is studied and a Monte Carlo study of power is performed.

Article information

Ann. Statist., Volume 15, Number 1 (1987), 420-426.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 62G10: Hypothesis testing

Counting process efficiency loss Kaplan-Meier estimator von Mises' statistical functional


Kumazawa, Yoshiki. On Testing Whether New is Better Than Used Using Randomly Censored Data. Ann. Statist. 15 (1987), no. 1, 420--426. doi:10.1214/aos/1176350276.

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