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September, 1961 Confidence Intervals from Censored Samples
Max Halperin
Ann. Math. Statist. 32(3): 828-837 (September, 1961). DOI: 10.1214/aoms/1177704976


Suppose a random sample of size $n$ is drawn from a normal population with mean $\mu$ and standard deviation $\sigma$ and that the sample has been censored either to the right or the left. Suppose the censoring is at a fixed point of the distribution or at a pre-specified sample percentage point, or is a combination of these two types of censoring. In this paper we present small sample bounded confidence intervals for $\mu$ and $\sigma$, based on a joint bounded confidence region at a confidence level with fixed bound. The limits for $\mu$ and $\sigma$ so obtained converge in probability, as $n \rightarrow \infty$, to the parameter values. The procedure of the paper allows similar results for some other scale-translation families of distributions. One such case, which is briefly discussed, is that of the exponential distribution with unknown initial point. The somewhat general applicability of the procedure mitigates the fact that it is not based on sufficient statistics.


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Max Halperin. "Confidence Intervals from Censored Samples." Ann. Math. Statist. 32 (3) 828 - 837, September, 1961.


Published: September, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0109.37705
MathSciNet: MR125676
Digital Object Identifier: 10.1214/aoms/1177704976

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 3 • September, 1961
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