In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case.
Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.
