TY - JOUR

T1 - D-optimal designs for quadratic mixture canonical polynomials with spline

AU - Zhang, Chongqi

AU - PENG, Heng

N1 - Funding Information:
We would like to thank the Referees and the journal editorial team for providing valuable advice that improved the quality of the original manuscript. This work is supported by National Nature Sciences Foundation of China (10871054) , CERG grants from the Hong Kong Research Grants Council ( HKBU 201610 and HKBU 201809 ), and FRG grants from Hong Kong Baptist University ( FRG/10-11/024 ).

PY - 2012/6

Y1 - 2012/6

N2 - Experiments with mixtures are special types of experiments in which the response depends only on the proportions of the input variables x=(x 1, ., x q) ', not on the total amount of ingredients. When a response variable cannot be adequately represented by a single polynomial function of the input variable over the entire experimental region, a possible solution is to use a regression model, termed the mixture polynomial with spline, which consists of grafted polynomial submodels. In this paper, we investigate a special mixture polynomial with spline in which the contribution of one ingredient proportion to the response variable, for example, x 1, is different from that of the others, as well as its D-optimal design for the entire experimental region.

AB - Experiments with mixtures are special types of experiments in which the response depends only on the proportions of the input variables x=(x 1, ., x q) ', not on the total amount of ingredients. When a response variable cannot be adequately represented by a single polynomial function of the input variable over the entire experimental region, a possible solution is to use a regression model, termed the mixture polynomial with spline, which consists of grafted polynomial submodels. In this paper, we investigate a special mixture polynomial with spline in which the contribution of one ingredient proportion to the response variable, for example, x 1, is different from that of the others, as well as its D-optimal design for the entire experimental region.

KW - D-optimality

KW - Mixture experiments

KW - Mixture polynomial with spline

UR - http://www.scopus.com/inward/record.url?scp=84858979148&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2012.02.013

DO - 10.1016/j.spl.2012.02.013

M3 - Article

AN - SCOPUS:84858979148

VL - 82

SP - 1095

EP - 1101

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 6

ER -