title: The Efficiency of Split Panel Designs in an Analysis of Variance Model.
abstract: We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm's efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution.
authors.affiliation: School of Economics and Management, Liaoning Shihua University, Fushun, China.
authors.forename: Xin
authors.identifier: 0000-0002-3498-4656
authors.initials: X
authors.lastname: Liu
authors.affiliation: School of Economics, Dongbei University of Finance and Economics, Dalian, China.
authors.forename: Wei-Guo
authors.initials: WG
authors.lastname: Wang
authors.affiliation: School of Marxism, Dalian Maritime University, Dalian, China.
authors.forename: Hai-Jun
authors.initials: HJ
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D005502:Food / Q000191:economics*; D006801:Humans; D015233:Models, Statistical; D009426:Netherlands; D012189:Retrospective Studies