Rasul A. Khan, "A note on Hammersley's inequality for estimating the normal integer mean", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 314030, 10 pages, 2003. https://doi.org/10.1155/S016117120320822X
A note on Hammersley's inequality for estimating the normal integer mean
Let be a random sample from a normal distribution with an unknown mean . Hammersley (1950) proposed the maximum likelihood estimator (MLE) , nearest integer to the sample mean, as an unbiased estimator of and extended the Cramér-Rao inequality. The Hammersley lower bound for the variance of any unbiased estimator of is significantly improved, and the asymptotic (as ) 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 is exhibited.
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