Optimality regions for designs in multiple linear regression models with correlated random coefficients

被引：1

作者：

Grasshoff, Ulrike ^{[1
]}

Holling, Heinz ^{[2
]}

Roettger, Frank ^{[3
,4
]}

Schwabe, Rainer ^{[3
]}

机构：

[1] Humboldt Univ, Wirtschaftswissensch Fak, Unter Linden 6, Berlin 10099, Germany

[2] Westfalische Wilhelms Univ Munster, Psychol Inst 4, Fliednerstr 21, Munster 48149, Germany

[3] Otto von Guericke Univ, Fak Math, Univ Pl 2, Magdeburg 39106, Germany

[4] MPI MiS Leipzig, Inselstr 22, Leipzig 04103, Germany

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2020年 / 209卷

关键词：

D-optimal design; Heteroscedastic model; Random coefficients; Multiple regression; Semi-algebraic geometry;

D O I：

10.1016/j.jspi.2020.04.004

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the D-optimality of a rhombic design via the Kiefer-Wolfowitz equivalence theorem. Subsequently, we show that the structure of an optimal rhombic design depends directly on the correlation structure of the random coefficients. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：267 / 279

页数：13

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