Asymptotic Expansion for a Class of Sample Quantiles
1982 ◽
Vol 31
(1-2)
◽
pp. 1-11
Keyword(s):
Let X k: n be the kth order statistic (1 ⩽ k ⩽ n) for a random sample of size n from a population with the distribution function F. Let {α n}, { βn} ( βn > 0) be sequences of real numbers and let { kn} ( kn ⩽ n) be a sequence of positive integers. The present article explores the various choices of α n, βn and kn such that under some mild regularity conditions on F, L( Yn) → n (0,1) as n→∞, where Yn = ( Xkn:n + α n)⁄ βn. It is further shown that under some additional conditions on F, standard asymptotic expansion (in Edgeworth form) for the distribution of Yn can be derived.
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1979 ◽
Vol 16
(02)
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pp. 445-448
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1976 ◽
Vol 13
(03)
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pp. 578-583
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1966 ◽
Vol 62
(4)
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pp. 637-642
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2014 ◽
Vol 11
(01)
◽
pp. 39-49
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2018 ◽
Vol 52
(4)
◽
pp. 1285-1313
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1985 ◽
Vol 28
(2)
◽
pp. 167-183
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