D-Optimal Chemical Balance Weighing Designs with N ≡ 0 (mod 4) and 3 Objects

In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were d...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2012-07, Vol.41 (13-14), p.2445-2455
Main Authors: Katulska, Krystyna, Smaga, Łukasz
Format: Article
Language:English
Subjects:
Chemical balance weighing design
Combinatorics
Combinatorics. Ordered structures
D-optimality
Designs and configurations
Exact sciences and technology
Experimental design
First-order autoregressive process
General topics
Mathematics
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were discussed in Li and Yang ( 2005 ) and also in Yeh and Lo Huang ( 2005 ). We present some results of D-optimal designs in certain class of designs with the design matrix X  ∈ M n×3 (±1) such that each column of matrix X has at least one 1 and one −1.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2011.608587