@article{oai:nagasaki-u.repo.nii.ac.jp:00023559,
 author = {Shikimi, Takuhisa},
 journal = {長崎大学経済学部研究年報},
 month = {Mar},
 note = {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., 長崎大学経済学部研究年報. vol.21, p.29-37; 2005},
 pages = {29--37},
 title = {Asymptotic normality for sums along data-dependent sampling schemes},
 volume = {21},
 year = {2005}
}