Exact Non-Parametric Confidence, Prediction and Tolerance Intervals with Progressive Type-II Censoring |
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Authors: | Olivier Guilbaud |
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Affiliation: | AstraZeneca, Sweden |
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Abstract: | Abstract. This article extends recent results [Scand. J. Statist. 28 (2001) 699] about exact non-parametric inferences based on order statistics with progressive type-II censoring. The extension lies in that non-parametric inferences are now covered where the dependence between involved order statistics cannot be circumvented. These inferences include: (a) tolerance intervals containing at least a specified proportion of the parent distribution, (b) prediction intervals containing at least a specified number of observations in a future sample, and (c) outer and/or inner confidence intervals for a quantile interval of the parent distribution. The inferences are valid for any parent distribution with continuous distribution function. The key result shows how the probability of an event involving k dependent order statistics that are observable/uncensored with progressive type-II censoring can be represented as a mixture with known weights of corresponding probabilities involving k dependent ordinary order statistics. Further applications/developments concerning exact Kolmogorov-type confidence regions are indicated. |
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Keywords: | confidence interval exact inference Kolmogorov-type confidence region mixture representation non-parametric order statistic prediction interval right censoring tolerance interval |
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