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	Balanced incomplete Latin square designs
	Ai, Mingyao ; Li, Kang ; Liu, Senmao ; Lin, Dennis K. J.
	2013
关键词	Balanced Incomplete Latin square Information matrix Optimality Orthogonal Latin square OPTIMALITY
英文摘要	Latin squares have been widely used to design an experiment where the blocking factors and treatment factors have the same number of levels. For some experiments, the size of blocks may be less than the number of treatments. Since not all the treatments can be compared within each block, a new class of designs called balanced incomplete Latin squares (BILS) is proposed. A general method for constructing BILS is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Latin squares. The optimality of the proposed BILS designs is investigated. It is shown that the proposed transversal BILS designs are asymptotically optimal for all the row, column and treatment effects. The relative efficiencies of a delete-one-transversal BILS design with respect to the optimal designs for both cases are also derived; it is shown to be close to 100%, as the order becomes large. (C) 2013 Elsevier B.V. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321599200015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Statistics & Probability; SCI(E); 6; ARTICLE; 9; 1575-1582; 143
语种	英语
出处	SCI
出版者	journal of statistical planning and inference
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157459]
专题	数学科学学院
推荐引用方式 GB/T 7714	Ai, Mingyao,Li, Kang,Liu, Senmao,et al. Balanced incomplete Latin square designs. 2013-01-01.

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