Abstract
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.
Keywords
MathematicsTruncation (statistics)StatisticsMaximum likelihoodRestricted maximum likelihoodVariance (accounting)Applied mathematicsMathematical proofExtension (predicate logic)Asymptotic distributionCombinatoricsEstimator
Related Publications
Bootstrap Methods: Another Look at the Jackknife
We discuss the following problem: given a random sample $\\mathbf{X} = (X_1, X_2, \\cdots, X_n)$ from an unknown probability distribution $F$, estimate the sampling distribution...
Order Statistics Estimators of the Location of the Cauchy Distribution
Abstract In a recent paper in this Journal, Rothenberg, Fisher and Tilanus [1] discuss a class of estimators of the location parameter of the Cauchy distribution, taking the for...
Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification.
This study evaluated the sensitivity of maximum likelihood (ML)-, generalized least squares (GLS)-, and asymptotic distribution-free (ADF)-based fit indices to model misspecific...
Estimating the Mean and Variance of Normal Populations from Singly Truncated and Doubly Truncated Samples
This paper is concerned with the problem of estimating the mean and variance of normal populations from singly and doubly truncated samples having known truncation points. Maxim...
Balanced Repeated Replications for Standard Errors
Abstract Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, an...
Publication Info
- Year
- 1952
- Type
- article
- Volume
- 23
- Issue
- 2
- Pages
- 226-238
- Citations
- 120
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
120
OpenAlex
Cite This
Max Halperin
(1952).
Maximum Likelihood Estimation in Truncated Samples.
The Annals of Mathematical Statistics
, 23
(2)
, 226-238.
https://doi.org/10.1214/aoms/1177729439
Identifiers
- DOI
- 10.1214/aoms/1177729439