Optimal design for prediction in multiresponse linear models based on rectangular confidence region

Xin Liu; Rong Xian Yue; Dennis K.J. Lin

doi:10.1016/j.jspi.2013.06.012

Optimal design for prediction in multiresponse linear models based on rectangular confidence region

Xin Liu, Rong Xian Yue, Dennis K.J. Lin

Statistics

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Abstract

This paper proposes a class of optimal design criteria for prediction in linear regression models with r responses based on the volume of the rectangular confidence region, termed RLr-optimality. A general equivalence theorem and a geometrical characterization of the R_L^r-optimal design are established, which are used to obtain or verify the R_L^r-optimality. Several examples are given for illustration.

Original language	English (US)
Pages (from-to)	1954-1967
Number of pages	14
Journal	Journal of Statistical Planning and Inference
Volume	143
Issue number	11
DOIs	https://doi.org/10.1016/j.jspi.2013.06.012
State	Published - Nov 2013

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/j.jspi.2013.06.012

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title = "Optimal design for prediction in multiresponse linear models based on rectangular confidence region",

abstract = "This paper proposes a class of optimal design criteria for prediction in linear regression models with r responses based on the volume of the rectangular confidence region, termed RLr-optimality. A general equivalence theorem and a geometrical characterization of the RLr-optimal design are established, which are used to obtain or verify the RLr-optimality. Several examples are given for illustration.",

author = "Xin Liu and Yue, {Rong Xian} and Lin, {Dennis K.J.}",

note = "Funding Information: This work was partially supported by NSFC Grants ( 11071168 , 11101077 , 11201062 ), Special Funds for Doctoral Authorities of Education Ministry ( 20103127110002 ), Innovation Program of Shanghai Municipal Education Commission ( 11zz116 ), E-Institutes of Shanghai Municipal Education Commission ( E03004 ), Shanghai Leading Academic Discipline Project , the Fundamental Research Funds for the Central Universities . ",

year = "2013",

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doi = "10.1016/j.jspi.2013.06.012",

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AU - Liu, Xin

AU - Yue, Rong Xian

AU - Lin, Dennis K.J.

N1 - Funding Information: This work was partially supported by NSFC Grants ( 11071168 , 11101077 , 11201062 ), Special Funds for Doctoral Authorities of Education Ministry ( 20103127110002 ), Innovation Program of Shanghai Municipal Education Commission ( 11zz116 ), E-Institutes of Shanghai Municipal Education Commission ( E03004 ), Shanghai Leading Academic Discipline Project , the Fundamental Research Funds for the Central Universities .

PY - 2013/11

Y1 - 2013/11

N2 - This paper proposes a class of optimal design criteria for prediction in linear regression models with r responses based on the volume of the rectangular confidence region, termed RLr-optimality. A general equivalence theorem and a geometrical characterization of the RLr-optimal design are established, which are used to obtain or verify the RLr-optimality. Several examples are given for illustration.

AB - This paper proposes a class of optimal design criteria for prediction in linear regression models with r responses based on the volume of the rectangular confidence region, termed RLr-optimality. A general equivalence theorem and a geometrical characterization of the RLr-optimal design are established, which are used to obtain or verify the RLr-optimality. Several examples are given for illustration.

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M3 - Article

AN - SCOPUS:84883304800

SN - 0378-3758

VL - 143

SP - 1954

EP - 1967

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 11

ER -

Optimal design for prediction in multiresponse linear models based on rectangular confidence region

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