D-optimality of the dual of BIB designs

BIB designs are shown to be D-optimal for the joint estimation of treatment contrasts and block contrasts over the class of all connected designs with v treatments in b blocks and a total of n observations. As a result, the dual of any BIB design is seen to be D-optimal for the estimation of treatme...

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Published inStatistics & probability letters Vol. 14; no. 3; pp. 201 - 203
Main Author Pohl, Gerhardt M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 24.06.1992
Elsevier
SeriesStatistics & Probability Letters
Subjects
BIB designs
D-optimality
D-optimality BIB designs dual designs two-factor designs
dual designs
Exact sciences and technology
Experimental design
Mathematics
Probability and statistics
Sciences and techniques of general use
Statistics
two-factor designs
BIB designs
dual designs
D-optimality
two-factor designs
Statistical contrast
Incomplete block design
Treatment
Balanced design
Optimal design
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Abstract BIB designs are shown to be D-optimal for the joint estimation of treatment contrasts and block contrasts over the class of all connected designs with v treatments in b blocks and a total of n observations. As a result, the dual of any BIB design is seen to be D-optimal for the estimation of treatment contrasts alone over the class of all connected designs with v treatments in b blocks of size k.
AbstractList BIB designs are shown to be D-optimal for the joint estimation of treatment contrasts and block contrasts over the class of all connected designs with v treatments in b blocks and a total of n observations. As a result, the dual of any BIB design is seen to be D-optimal for the estimation of treatment contrasts alone over the class of all connected designs with v treatments in b blocks of size k.
BIB designs are shown to be D-optimal for the joint estimation of treatment contrasts and block contrasts over the class of all connected designs with v treatments in b blocks and a total of n observations. As a result, the dual of any BIB design is seen to be D-optimal for the estimation of treatment contrasts alone over the class of all connected designs with v treatments in b blocks of size k.
Author Pohl, Gerhardt M.
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10.1016/0378-3758(85)90044-8
10.1016/0167-7152(91)90139-I
10.1214/aos/1176343420
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Issue 3
Keywords BIB designs
dual designs
D-optimality
two-factor designs
Statistical contrast
Incomplete block design
Treatment
Balanced design
Optimal design
Language English
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References Jacroux (BIB5) 1985; 11
Kiefer (BIB6) 1975
Eccleston, Kiefer (BIB2) 1991; 5
Shah, Raghavarao, Khatri (BIB7) 1976; 4
Shah, Sinha (BIB8) 1989
John, Mitchell (BIB4) 1977; 39
Cheng (BIB1) 1980; 2
Gupta, Das, Dey (BIB3) 1991; 11
Gupta (10.1016/0167-7152(92)90022-W_BIB3) 1991; 11
John (10.1016/0167-7152(92)90022-W_BIB4) 1977; 39
Jacroux (10.1016/0167-7152(92)90022-W_BIB5) 1985; 11
Kiefer (10.1016/0167-7152(92)90022-W_BIB6) 1975
Eccleston (10.1016/0167-7152(92)90022-W_BIB2) 1991; 5
Shah (10.1016/0167-7152(92)90022-W_BIB8) 1989
Cheng (10.1016/0167-7152(92)90022-W_BIB1) 1980; 2
Shah (10.1016/0167-7152(92)90022-W_BIB7) 1976; 4
References_xml – volume: 11
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  year: 1991
  end-page: 180
  ident: BIB3
  article-title: Universal Optimality of block designs with unequal block sizes
  publication-title: Statist. Probab. Lett.
  contributor:
    fullname: Dey
– volume: 5
  start-page: 213
  year: 1991
  end-page: 219
  ident: BIB2
  article-title: Relationships of optimality for individual factors of a design
  publication-title: J. Statist. Plann. Inference
  contributor:
    fullname: Kiefer
– start-page: 333
  year: 1975
  end-page: 353
  ident: BIB6
  article-title: Construction and optimality of generalized Youden designs
  publication-title: A Survey of Statistical Design and Linear Models
  contributor:
    fullname: Kiefer
– volume: 4
  start-page: 419
  year: 1976
  end-page: 422
  ident: BIB7
  article-title: Optimality of two and three factor designs
  publication-title: Ann. Statist.
  contributor:
    fullname: Khatri
– volume: 39
  start-page: 39
  year: 1977
  end-page: 43
  ident: BIB4
  article-title: Optimal incomplete block designs
  publication-title: J. Roy. Statist. Soc. Ser. B
  contributor:
    fullname: Mitchell
– volume: 11
  start-page: 385
  year: 1985
  end-page: 398
  ident: BIB5
  article-title: Some sufficient conditions for the Type 1 optimality of block designs
  publication-title: J. Statist. Plann. Inference
  contributor:
    fullname: Jacroux
– volume: 2
  start-page: 199
  year: 1980
  end-page: 204
  ident: BIB1
  article-title: On the E-optimality of some block designs
  publication-title: J. Roy. Statist. Soc.
  contributor:
    fullname: Cheng
– year: 1989
  ident: BIB8
  publication-title: Theory of Optimal Designs
  contributor:
    fullname: Sinha
– volume: 5
  start-page: 213
  year: 1991
  ident: 10.1016/0167-7152(92)90022-W_BIB2
  article-title: Relationships of optimality for individual factors of a design
  publication-title: J. Statist. Plann. Inference
  doi: 10.1016/0378-3758(81)90001-X
  contributor:
    fullname: Eccleston
– volume: 39
  start-page: 39
  year: 1977
  ident: 10.1016/0167-7152(92)90022-W_BIB4
  article-title: Optimal incomplete block designs
  publication-title: J. Roy. Statist. Soc. Ser. B
  contributor:
    fullname: John
– start-page: 333
  year: 1975
  ident: 10.1016/0167-7152(92)90022-W_BIB6
  article-title: Construction and optimality of generalized Youden designs
  contributor:
    fullname: Kiefer
– year: 1989
  ident: 10.1016/0167-7152(92)90022-W_BIB8
  contributor:
    fullname: Shah
– volume: 11
  start-page: 385
  year: 1985
  ident: 10.1016/0167-7152(92)90022-W_BIB5
  article-title: Some sufficient conditions for the Type 1 optimality of block designs
  publication-title: J. Statist. Plann. Inference
  doi: 10.1016/0378-3758(85)90044-8
  contributor:
    fullname: Jacroux
– volume: 11
  start-page: 177
  year: 1991
  ident: 10.1016/0167-7152(92)90022-W_BIB3
  article-title: Universal Optimality of block designs with unequal block sizes
  publication-title: Statist. Probab. Lett.
  doi: 10.1016/0167-7152(91)90139-I
  contributor:
    fullname: Gupta
– volume: 4
  start-page: 419
  issue: 2
  year: 1976
  ident: 10.1016/0167-7152(92)90022-W_BIB7
  article-title: Optimality of two and three factor designs
  publication-title: Ann. Statist.
  doi: 10.1214/aos/1176343420
  contributor:
    fullname: Shah
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  article-title: On the E-optimality of some block designs
  publication-title: J. Roy. Statist. Soc.
  contributor:
    fullname: Cheng
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Snippet BIB designs are shown to be D-optimal for the joint estimation of treatment contrasts and block contrasts over the class of all connected designs with v...
BIB designs are shown to be D-optimal for the joint estimation of treatment contrasts and block contrasts over the class of all connected designs with v...
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SubjectTerms BIB designs
D-optimality
D-optimality BIB designs dual designs two-factor designs
dual designs
Exact sciences and technology
Experimental design
Mathematics
Probability and statistics
Sciences and techniques of general use
Statistics
two-factor designs
Title D-optimality of the dual of BIB designs
URI https://dx.doi.org/10.1016/0167-7152(92)90022-W
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Volume 14
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