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June, 1952 Maximum Likelihood Estimation in Truncated Samples
Max Halperin
Ann. Math. Statist. 23(2): 226-238 (June, 1952). DOI: 10.1214/aoms/1177729439


In this paper we consider the problem of estimation of parameters from a sample in which only the first $r$ (of $n$) ordered observations are known. If $r = \lbrack qn \rbrack, 0 < q < 1$, it is shown under mild regularity conditions, for the case of one parameter, that estimation of $\theta$ by maximum likelihood is best in the sense that $\hat{\theta}$, the maximum likelihood estimate of $\theta$, is (a) consistent, (b) asymptotically normally distributed, (c) of minimum variance for large samples. A general expression for the variance of the asymptotic distribution of $\hat{\theta}$ is obtained and small sample estimation is considered for some special choices of frequency function. Results for two or more parameters and their proofs are indicated and a possible extension of these results to more general truncation is suggested.


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Max Halperin. "Maximum Likelihood Estimation in Truncated Samples." Ann. Math. Statist. 23 (2) 226 - 238, June, 1952.


Published: June, 1952
First available in Project Euclid: 28 April 2007

zbMATH: 0047.13302
MathSciNet: MR48760
Digital Object Identifier: 10.1214/aoms/1177729439

Rights: Copyright © 1952 Institute of Mathematical Statistics

Vol.23 • No. 2 • June, 1952
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