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- W1536618208 abstract "Consider distribution functions F and G and suppose that F(x) < G(x) for all x. The problem of estimating F or G, or both, arises quite naturally in applications. For example, in corrosion engineering it is of interest to estimate the pitting times of metals under two different strengths of corrosive environments. The empirical distribution functions Fm and Gn will not necessary satisfy the order constraint imposed by the experimental conditions. Lo (1987) proposed the estimators Fm = min(Fm,Gn) and Gn = max(Fm,Gn), which satisfy the constraint of interest, and showed that these estimator are asymptotically minimax, under suitable conditions, for a large class of loss functions. Although Fm and Gn are strongly uniformly consistent when both m and ? tend to infinity, neither one is when only m or ? go to infinity. Here, the estimators F^ (G*) are proposed which are strongly uniformly consistent for F (G) when only m (?) ?? oo. The case of censored data is also considered. Under suitable conditions, weak convergence of the processes {y/m(Fn(x) F(x)), 0 < ? < oo, m = 1,...} and {V?(G* (x) G(x)), 0 < ? < oc, ? = 1,...} is demonstrated. As a consequence, asymptotic confidence bands are obtained. For testing the hypothesis of identical distributions against a stochastic order alternative, the asymptotic distribution of the estimators under the assumption that F(x) = G(x) for all ? is also discussed. The results of a Monte-Carlo study show that the new estimators perform better than Fm and Gn and the non-parametric maximum likelihood estimators in terms of bias and mean squared error for a large class of examples." @default.
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- W1536618208 date "2004-01-01" @default.
- W1536618208 modified "2023-09-23" @default.
- W1536618208 title "On the estimation of survival functions under a stochastic order constraint" @default.
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- W1536618208 doi "https://doi.org/10.1214/lnms/1215006764" @default.
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