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Asymptotic normality for sums along data-dependent sampling schemes


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Title: Asymptotic normality for sums along data-dependent sampling schemes
Other Titles: Asymptotic normality for sums along data-dependent sampling schemes
Authors: Shikimi, Takuhisa
Authors (alternative): 式見, 拓仙
Issue Date: 25-Mar-2005
Citation: 長崎大学経済学部研究年報. vol.21, p.29-37; 2005
Abstract: Let X_<(1)>={X_<1,t^1>,t^1∈N},..., X_<(d)>={X_<d,t^d>, t^d∈N} be independent sequences of i.i.d. real-valued random variables and let S_t=S_<1,t>+…+S_<d,t^d> where t=(t^1,...,t^d) and S_<i,t^i>=Σ_<s^i>≤t^i-μ_i)/σ_i), i=1,...,d. A sequential sampling plan determines the way of taking one observation from one of the processes X_<()>,...,X_<(d)>, according to the previous sampled data. We show that the random sum of observations under any sequential sampling scheme is asymptotically normal. An easy application of the normality yields the classical result of sequential interval estimation of means of two polulations.
Keywords: asymptotic normality / sequential sampling plan / sequential interval estimation
URI: http://hdl.handle.net/10069/6887
ISSN: 09108602
Type: Departmental Bulletin Paper
Appears in Collections:Volume 21

Citable URI : http://hdl.handle.net/10069/6887

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