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| CONVERGENCE ON RANDOMLY TRIMMED SUMS WITH A DEPENDENT SAMPLE |
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Citation： |
Lin Zhengyan.CONVERGENCE ON RANDOMLY TRIMMED SUMS WITH A DEPENDENT SAMPLE[J].Chinese Annals of Mathematics B,1998,19(3):281~292 |
| Page view： 975
Net amount： 768 |
Authors： |
Lin Zhengyan; |
Foundation： |
Project supported by the National Natural Science
Foundation of China and the Natural Science Foundation of Zhejiang Province. |
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| Abstract： |
Let $ \{X_n\} $ be a sequence of random variables and
$ X_{n1}\le{X_{n2}}\le\cdots \le{X_{nn}} $ their order statistics.
In this paper a central limit theorem and a strong law of large numbers for
randomly trimmed sums $T_n =\sum_{i=\alpha_n+1}^{\beta_n}\limits X_{ni}$
are established in the case that $\alpha_n$ and $\beta_n$ are positive
integer-valued random variables such that $\alpha_n/n$ and $\beta_n/n$
converge to random variables $\alpha$ and $\beta$ respectively with
$0\le\alpha<\beta\le1$ in certain sense, and $\{X_n\}$ is a
$\varphi$-mixing sequence. |
Keywords： |
Randomly trimmed sums, $\varphi$-mixing,
a.s.convergence, Asymptotic normality |
Classification： |
60F05, 60G50 |
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