The Annals of Mathematical Statistics

Non-Parametric Estimation. I. Validation of Order Statistics

H. Scheffe and J. W. Tukey

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Previous work on non-parametric estimation has concerned three problems: (i) confidence intervals for an unknown quantile, (ii) population tolerance limits, (iii) confidence bands of an unknown cumulative distribution function $(cdf)$. For problem (iii) a solution has been available which is valid for any $cdf$ whatever, but for (i) and (ii) it has heretofore assumed that the population has continuous probability density. This paper validates the existing solutions of (i) and (ii) assuming only a continuous $cdf$. It then modifies these solutions so that they are valid for any $cdf$ whatever.

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Ann. Math. Statist., Volume 16, Number 2 (1945), 187-192.

First available in Project Euclid: 28 April 2007

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Scheffe, H.; Tukey, J. W. Non-Parametric Estimation. I. Validation of Order Statistics. Ann. Math. Statist. 16 (1945), no. 2, 187--192. doi:10.1214/aoms/1177731119.

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See also

  • Part II: John W. Tukey. Non-Parametric Estimation II. Statistically Equivalent Blocks and Tolerance Regions--The Continuous Case. Ann. Math. Statist., Volume 18, Number 4 (1947), 529--539.
  • Part III: John W. Tukey. Nonparametric Estimation, III. Statistically Equivalent Blocks and Multivariate Tolerance Regions--The Discontinuous Case. Ann. Math. Statist., Volume 19, Number 1 (1948), 30--39.