A note on Hammersley%26apos;s inequality for estimating the normal integer mean

作者:Rasul A Khan
来源:International Journal of Mathematics and Mathematical Sciences, 2003.
DOI:10.1155/s016117120320822x

摘要

Let X1,X2,%26#8230;,Xn be a random sample from a normal N(%26#952;,%26#963;2) distribution with an unknown mean %26#952;=0,%26#177;1,%26#177;2,%26#8230;. Hammersley (1950) proposed the maximum likelihood estimator (MLE) d=[X%26#175;n], nearest integer to the sample mean, as an unbiased estimator of %26#952; and extended the Cram%26#233;r-Rao inequality. The Hammersley lower bound for the variance of any unbiased estimator of %26#952; is significantly improved, and the asymptotic (as n%26#8594;%26#8734;) 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.

  • 出版日期2003

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