Abstract
Abstract Let Tj be a reasonable estimator (for example, a minimum mean square error estimator) of the parameter θ of the family Dj of distributions, j = 1, 2, …, m. An estimator T, which is a weighted mean of T 1, T s, …, Tm , is found that has the same asymptotic distribution as that of Tj , when the sample comes from Dj , j = 1, 2, …, m. Here the weights are functions of the sample items. Empirical evidence is given which indicates that T is satisfactory for small sample sizes. It is proved that if Tj and the weight Wj are odd location and even location-free statistics, respectively, j = 1, 2, …, m, then T = ΣWiTi , where ΣWi = 1, is an unbiased estimator of the center of every symmetric distribution, provided certain expectations exist. This is useful in the construction of the weight function Wj.
Keywords
EstimatorMathematicsStatisticsMean squared errorEfficient estimatorEmpirical distribution functionWeight functionMinimum-variance unbiased estimatorConsistent estimatorBias of an estimatorSample (material)CombinatoricsU-statisticPhysics
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Publication Info
- Year
- 1967
- Type
- article
- Volume
- 62
- Issue
- 320
- Pages
- 1179-1186
- Citations
- 140
- Access
- Closed
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Cite This
Robert V. Hogg
(1967).
Some Observations on Robust Estimation.
Journal of the American Statistical Association
, 62
(320)
, 1179-1186.
https://doi.org/10.1080/01621459.1967.10500924
Identifiers
- DOI
- 10.1080/01621459.1967.10500924