×

Unbiased inestimability of the larger of two parameters. (English) Zbl 0811.62028

Summary: S. Blumenthal and A. Cohen [J. Am. Stat. Assoc. 63, 861-876 (1968)] and I. D. Dhariyal, D. Sharma and K. Krishnamoorthy [Statistics 16, 89-95 (1985; Zbl 0562.62026)] considered the question of the existence of unbiased estimators of the larger (smaller) of two parameters.
We first show the non-existence of such an unbiased estimator in case of two double exponential populations with unknown locations. We also give a general inestimability result and apply it to the uniform distribution.

MSC:

62F10 Point estimation
62F30 Parametric inference under constraints
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barlow R. E., Statistical Inference Under Order Restrictions (1972)
[2] DOI: 10.1214/aoms/1177698413 · Zbl 0187.15602 · doi:10.1214/aoms/1177698413
[3] DOI: 10.1214/aoms/1177698414 · Zbl 0187.15601 · doi:10.1214/aoms/1177698414
[4] DOI: 10.2307/2283879 · Zbl 0162.49705 · doi:10.2307/2283879
[5] DOI: 10.1214/aoms/1177696702 · Zbl 0224.62006 · doi:10.1214/aoms/1177696702
[6] DOI: 10.1080/02331888508801827 · Zbl 0562.62026 · doi:10.1080/02331888508801827
[7] DOI: 10.1007/BF01111206 · Zbl 0203.51404 · doi:10.1007/BF01111206
[8] Dudewicz E. J., Trabajos de Estadistica 19 pp 65– (1971)
[9] Dudewicz E. J., Tamkang J. Math. 3 pp 101– (1972)
[10] DOI: 10.1007/BF02479392 · Zbl 0344.62026 · doi:10.1007/BF02479392
[11] Halmos P. R., Measure Theory (1952)
[12] DOI: 10.1080/03610928808829876 · Zbl 0696.62114 · doi:10.1080/03610928808829876
[13] DOI: 10.1080/03610928908830148 · Zbl 0696.62115 · doi:10.1080/03610928908830148
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.