A note on Hammersley's inequality for estimating the normal integer mean

Rasul A. Khan

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-10

Abstract:

Let X 1 , X 2 , … , X n be a random sample from a normal N ( θ , σ 2 ) distribution with an unknown mean θ = 0 , ± 1 , ± 2 , … . Hammersley (1950) proposed the maximum likelihood estimator (MLE) d = [ X ¯ n ] , nearest integer to the sample mean, as an unbiased estimator of θ and extended the Cramér-Rao inequality. The Hammersley lower bound for the variance of any unbiased estimator of θ is significantly improved, and the asymptotic (as n → ∞ ) limit of Fraser-Guttman-Bhattacharyya bounds is also determined. A limiting property of a suitable distance is used to give some plausible explanations why such bounds cannot be attained. An almost uniformly minimum variance unbiased (UMVU) like property of d is exhibited.

Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/314030.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/314030.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:314030

DOI: 10.1155/S016117120320822X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().