Abstract
We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 30-56 |
| Number of pages | 27 |
| Journal | Annals of Statistics |
| Volume | 43 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 1 2015 |
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Keywords
- Chebyshev system
- Complete class
- Generalized linear model
- Locally optimal design
- Nonlinear model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Saturated locally optimal designs under differentiable optimality criteria. / Linwei, H. U.; Yang, Min; Stufken, John.
In: Annals of Statistics, Vol. 43, No. 1, 01.02.2015, p. 30-56.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Saturated locally optimal designs under differentiable optimality criteria
AU - Linwei, H. U.
AU - Yang, Min
AU - Stufken, John
PY - 2015/2/1
Y1 - 2015/2/1
N2 - We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.
AB - We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.
KW - Chebyshev system
KW - Complete class
KW - Generalized linear model
KW - Locally optimal design
KW - Nonlinear model
UR - http://www.scopus.com/inward/record.url?scp=84922573408&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84922573408&partnerID=8YFLogxK
U2 - 10.1214/14-AOS1263
DO - 10.1214/14-AOS1263
M3 - Article
VL - 43
SP - 30
EP - 56
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 1
ER -