Admissibility and minimaxity of the uniform design measure in nonparametric regression model

Min Yu Xie; Kai Tai Fang

doi:10.1016/s0378-3758(99)00089-0

Admissibility and minimaxity of the uniform design measure in nonparametric regression model

Min Yu Xie^*, Kai Tai Fang

^*Corresponding author for this work

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

34 Citations (Scopus)

Abstract

This paper studies the optimal design problem of a nonparametric regression model. A frame of the decision theory for nonparametric experimental designs is set up. Under this frame, the admissible minimaxity of the uniform design measure π, which has a constant density over the experimental domain, is obtained. Furthermore, we prove that π is the best design among a reasonable subclass of designs.

Original language	English
Pages (from-to)	101-111
Number of pages	11
Journal	Journal of Statistical Planning and Inference
Volume	83
Issue number	1
DOIs	https://doi.org/10.1016/s0378-3758(99)00089-0
Publication status	Published - 1 Jan 2000
Externally published	Yes

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

User-Defined Keywords

62K05
62K99
Apporximately linear model
Decision theory
Nonparametric regression model
Optimal design
Uniform design
Uniform design measure

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10.1016/s0378-3758(99)00089-0

Cite this

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abstract = "This paper studies the optimal design problem of a nonparametric regression model. A frame of the decision theory for nonparametric experimental designs is set up. Under this frame, the admissible minimaxity of the uniform design measure π, which has a constant density over the experimental domain, is obtained. Furthermore, we prove that π is the best design among a reasonable subclass of designs.",

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author = "Xie, {Min Yu} and Fang, {Kai Tai}",

note = "Funding Information: This work was partially supported by a Chinese National Natural Science Foundation grant and a Hong Kong UGC grant. The authors are thankful to Dr. Fred J. Hickernell for his comments.",

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AU - Xie, Min Yu

AU - Fang, Kai Tai

N1 - Funding Information: This work was partially supported by a Chinese National Natural Science Foundation grant and a Hong Kong UGC grant. The authors are thankful to Dr. Fred J. Hickernell for his comments.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - This paper studies the optimal design problem of a nonparametric regression model. A frame of the decision theory for nonparametric experimental designs is set up. Under this frame, the admissible minimaxity of the uniform design measure π, which has a constant density over the experimental domain, is obtained. Furthermore, we prove that π is the best design among a reasonable subclass of designs.

AB - This paper studies the optimal design problem of a nonparametric regression model. A frame of the decision theory for nonparametric experimental designs is set up. Under this frame, the admissible minimaxity of the uniform design measure π, which has a constant density over the experimental domain, is obtained. Furthermore, we prove that π is the best design among a reasonable subclass of designs.

KW - 62K05

KW - 62K99

KW - Apporximately linear model

KW - Decision theory

KW - Nonparametric regression model

KW - Optimal design

KW - Uniform design

KW - Uniform design measure

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VL - 83

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EP - 111

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 1

ER -

Admissibility and minimaxity of the uniform design measure in nonparametric regression model

Abstract

Scopus Subject Areas

User-Defined Keywords

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