<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In the paper we consider the linear regression model of the first degree on the vertices of the d-dimensional unit cube and its extension by an intercept term, which can be used, e.g., to model unbiased or biased weighing of d objects on a spring balance. In both settings, we can restrict our search for approximate optimal designs to the convex combinations of the so-called j-vertex designs. We focus on the designs that are criterion robust in the sense of maximin efficiency within the class of all orthogonally invariant information functions, involving the criteria of D-, A-, E-optimality, and many others. For the model of unbiased weighing, we give analytic formulas for the maximin efficient design, and for the biased model we present numerical results based on the application of the methods of semidefinite programming.</p></abstract>

In the paper we consider the linear regression model of the first degree on the vertices of the d-dimensional unit cube and its extension by an intercept term, which can be used, e.g., to model unbiased or biased weighing of d objects on a spring balance. In both settings, we can restrict our search for approximate optimal designs to the convex combinations of the so-called j-vertex designs. We focus on the designs that are criterion robust in the sense of maximin efficiency within the class of all orthogonally invariant information functions, involving the criteria of D-, A-, E-optimality, and many others. For the model of unbiased weighing, we give analytic formulas for the maximin efficient design, and for the biased model we present numerical results based on the application of the methods of semidefinite programming.

Criterion-robust designs for the models of spring balance weighing

Department of Applied Mathematics and Statistics Faculty of Mathematics, Physics and Informatics Comenius University Mlynsk´a dolina SK–842-48 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Criterion-robust designs for the models of spring balance weighing"}

In the paper we consider the linear regression model of the first degree on the vertices of the d-dimensional unit cube and its extension by an intercept term,...

Criterion-robust designs for the models of spring balance weighing

Published Online: Nov 13, 2012

Page range: 23 - 32

DOI: https://doi.org/10.2478/v10127-012-0003-2

Keywords
spring balance weighing, optimal design, maximin efficiency.

This content is open access.

Criterion-robust designs for the models of spring balance weighing

Published Online: Nov 13, 2012

Page range: 23 - 32

DOI: https://doi.org/10.2478/v10127-012-0003-2

Keywordsspring balance weighing, optimal design, maximin efficiency.

This content is open access.

Keywords
spring balance weighing, optimal design, maximin efficiency.