Limit theorems for trimmed sums |
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| Authors: | Yuji Kasahara Makoto Maejima |
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| Institution: | (1) Institute of Mathematics, University of Tsukuba, 305 Tsukuba, Ibaraki, Japan;(2) Department of Mathematics, Keio University, 223 Hiyoshi, Yokohama, Japan |
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| Abstract: | This paper studies the heavily trimmed sums (*) 
ns] + 1
nt]
X
j
(n)
, where {X
j
(n)
}
j = 1
n
are the order statistics from independent random variables {X
1,...,X
n
} having a common distributionF. The main theorem gives the limiting process of (*) as a process oft. More smoothly trimmed sums like
j = 1
nt]
J(j/n)X
j
(n)
are also discussed. |
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| Keywords: | Heavily trimmed sums Brownian bridge smoothly trimmed sums |
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