Clear effects criterion is an important criterion for selecting fractional factorial designs[1].Tang et al.[2]derived upper and lower bounds on the maximum number of clear two-factor interactions（2fi＇s）in 2^n-（n-k）designs of resolution Ⅲ and Ⅳ by constructing 2^n-（n-k）designs.But the method in[2]does not perform well sometimes when the resolution is Ⅲ.This article modifies the construction method for 2^n-（n-k） designs of resolution Ⅲ in[2].The modified method is a great improvement on that used in[2].
This paper gets some necessary conditions for the existence of some kinds of clear 4^m2^n compromise plans which allow estimation of all main effects and some specified two-factor interactions without assuming the remaining two-factor interactions being negligible. Some methods for constructing clear 4^m2^n compromise plans are introduced.
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.
In this paper we use profile empirical likelihood to construct confidence regions for regression coefficients in partially linear model with longitudinal data. The main contribution is that the within-subject correlation is considered to improve estimation efficiency. We suppose a semi-parametric structure for the covariances of observation errors in each subject and employ both the first order and the second order moment conditions of the observation errors to construct the estimating equations. Although there are nonparametric variable in distribution after estimators, the empirical log-likelihood ratio statistic still tends to a standard Xp2 the nuisance parameters are profiled away. A data simulation is also conducted.
