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| ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES |
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Citation： |
Wei Laisheng.ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES[J].Chinese Annals of Mathematics B,1989,10(1):94~104 |
| Page view： 820
Net amount： 699 |
Authors： |
Wei Laisheng; |
Foundation： |
Projects supported by the Science Fund of the Chinese Academy of Sciences. |
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| Abstract： |
Consider the two-sided truncation distrbution families written in the form
$$\[f(x,\theta )dx = \omega ({\theta _1},{\theta _2})h(x){I_{[{\theta _1},{\theta _2}]}}(x)dx,\theta = ({\theta _1},{\theta _2}).\]$$
$$\[T(x) = ({t_1}(x),{t_2}(x)) = (\min ({x_1}, \cdots {x_m}),\max ({x_1}, \cdots {x_m}))\]$$
is a sufficient statistic and its marginal density is denoted by $\[f(t)d{\mu ^T}\]$. The prior distribution of $\[\theta \]$ belongs to the family
$$\[F = \{ G:{\int {\int {\left\| \theta \right\|} } ^2}dG(\theta ) < \infty \} \]$$
In this paper, the author constructs the empirical Bayes estimator (EBE) of $\[\theta \]$, $\[{\phi _n}(t)\]$, by using the kernel estimation of $\[f(t)\]$. Under a quite general assumption imposed upon $\[f(t)\]$
and $\[h(x)\]$, it is shown that $\[{\phi _n}(t)\]$ is an asymptotically optimal EBE of $\[\theta \]$. |
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