## The Annals of Mathematical Statistics

### Non-Parametric Estimation. I. Validation of Order Statistics

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177731119

Digital Object Identifier
doi:10.1214/aoms/1177731119

Mathematical Reviews number (MathSciNet)
MR12404

Zentralblatt MATH identifier
0060.30511

JSTOR