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| ON ONE CONJECTURE OF R. S. SINGH |
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Citation： |
Chen Xiru.ON ONE CONJECTURE OF R. S. SINGH[J].Chinese Annals of Mathematics B,1983,4(2):193~198 |
| Page view： 750
Net amount： 671 |
Authors： |
Chen Xiru; |
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| Abstract： |
In 1979 R. S. Singh (Ann, Statist, 1979, p. 890) made a conjecture concerning the convergence rate of EB estimates of the parameter $\[\theta \]$ in an one-dimensional continuous exponential distribution family, under the square loss function, the prior distribution family
being confined to a bounded interval. The conjecture asserts that the rate cannot reach $\[o({\raise0.7ex\hbox{$1$} \!\mathord{\left/
{\vphantom {1 n}}\right.\kern-\nulldelimiterspace}
\!\lower0.7ex\hbox{$n$}})\]$
or even $\[O({\raise0.7ex\hbox{$1$} \!\mathord{\left/
{\vphantom {1 n}}\right.\kern-\nulldelimiterspace}
\!\lower0.7ex\hbox{$n$}})\]$. In this article, the weaker part of this conjecture (i, e. the $\[o({\raise0.7ex\hbox{$1$} \!\mathord{\left/
{\vphantom {1 n}}\right.\kern-\nulldelimiterspace}
\!\lower0.7ex\hbox{$n$}})\]$ part) is shown to be correct. |
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