Lower bounds of various criteria in experimental designs

Kai Tai Fang; Yu Tang; Jianxing Yin

doi:10.1016/j.jspi.2007.05.013

Lower bounds of various criteria in experimental designs

Kai Tai Fang^*, Yu Tang, Jianxing Yin

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

12 Citations (Scopus)

16 Downloads (Pure)

Abstract

Criterion is essential for measuring the goodness of an experimental design. In this paper, lower bounds of various criteria in experimental designs will be reviewed according to methodology of their construction. The criteria include most well-known ones which are frequently used as benchmarks for orthogonal array, uniform design, supersaturated design and other types of designs. To derive the lower bounds of these criteria, five different approaches are explored. Some new results are given. Throughout the paper, some relationships among different types of lower bounds are also discussed.

Original language	English
Pages (from-to)	184-195
Number of pages	12
Journal	Journal of Statistical Planning and Inference
Volume	138
Issue number	1
DOIs	https://doi.org/10.1016/j.jspi.2007.05.013
Publication status	Published - 1 Jan 2008
Externally published	Yes

User-Defined Keywords

Fractional factorial design
Lower bound
Supersaturated design
Uniform design

Access to Document

10.1016/j.jspi.2007.05.013

Full TextAccepted author manuscript, 1.04 MB

Cite this

@article{74c8e8bacaa64ddbb2b5b8abc2e9d7e9,

title = "Lower bounds of various criteria in experimental designs",

abstract = "Criterion is essential for measuring the goodness of an experimental design. In this paper, lower bounds of various criteria in experimental designs will be reviewed according to methodology of their construction. The criteria include most well-known ones which are frequently used as benchmarks for orthogonal array, uniform design, supersaturated design and other types of designs. To derive the lower bounds of these criteria, five different approaches are explored. Some new results are given. Throughout the paper, some relationships among different types of lower bounds are also discussed.",

keywords = "Fractional factorial design, Lower bound, Supersaturated design, Uniform design",

author = "Fang, {Kai Tai} and Yu Tang and Jianxing Yin",

note = "Funding Information: We would thank Fred J. Hickernell, Dennis, K.J. Lin and Rahul Mukerjee's valuable comments. The authors would like to thank the anonymous referee for their constructive comments. Fang's research was partially supported by the Hong Kong RGC grant RGC/HKBU 200804, Hong Kong Baptist University FRG grant FRG/03-04/II-711, and Yin's research was supported by an NSF Grant 10371086.",

year = "2008",

month = jan,

day = "1",

doi = "10.1016/j.jspi.2007.05.013",

language = "English",

volume = "138",

pages = "184--195",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Lower bounds of various criteria in experimental designs

AU - Fang, Kai Tai

AU - Tang, Yu

AU - Yin, Jianxing

N1 - Funding Information: We would thank Fred J. Hickernell, Dennis, K.J. Lin and Rahul Mukerjee's valuable comments. The authors would like to thank the anonymous referee for their constructive comments. Fang's research was partially supported by the Hong Kong RGC grant RGC/HKBU 200804, Hong Kong Baptist University FRG grant FRG/03-04/II-711, and Yin's research was supported by an NSF Grant 10371086.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - Criterion is essential for measuring the goodness of an experimental design. In this paper, lower bounds of various criteria in experimental designs will be reviewed according to methodology of their construction. The criteria include most well-known ones which are frequently used as benchmarks for orthogonal array, uniform design, supersaturated design and other types of designs. To derive the lower bounds of these criteria, five different approaches are explored. Some new results are given. Throughout the paper, some relationships among different types of lower bounds are also discussed.

AB - Criterion is essential for measuring the goodness of an experimental design. In this paper, lower bounds of various criteria in experimental designs will be reviewed according to methodology of their construction. The criteria include most well-known ones which are frequently used as benchmarks for orthogonal array, uniform design, supersaturated design and other types of designs. To derive the lower bounds of these criteria, five different approaches are explored. Some new results are given. Throughout the paper, some relationships among different types of lower bounds are also discussed.

KW - Fractional factorial design

KW - Lower bound

KW - Supersaturated design

KW - Uniform design

UR - http://www.scopus.com/inward/record.url?scp=34548831077&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2007.05.013

DO - 10.1016/j.jspi.2007.05.013

M3 - Journal article

AN - SCOPUS:34548831077

SN - 0378-3758

VL - 138

SP - 184

EP - 195

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 1

ER -

Lower bounds of various criteria in experimental designs

Abstract

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this