D-optimal chemical balance weighing designs with autoregressive errors

Krystyna Katulska () and Łukasz Smaga ()

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 3, 393-407

Abstract: In this paper, we consider the estimation problem of individual weights of three objects. For the estimation we use the chemical balance weighing design and the criterion of D-optimality. We assume that the error terms $${\varepsilon_{i},\ i=1,2,\dots,n,}$$ are a first-order autoregressive process. This assumption implies that the covariance matrix of errors depends on the known parameter ρ. We present the chemical balance weighing design matrix $${\widetilde{\bf X}}$$ and we prove that this design is D-optimal in certain classes of designs for $${\rho\in[0,1)}$$ and it is also D-optimal in the class of designs with the design matrix $${{\bf X} \in M_{n\times 3}(\pm 1)}$$ for some ρ ≥ 0. We prove also the necessary and sufficient conditions under which the design is D-optimal in the class of designs $${M_{n\times 3}(\pm 1)}$$ , if $${\rho\in[0,1/(n-2))}$$ . We present also the matrix of the D-optimal factorial design with 3 two-level factors. Copyright The Author(s) 2013

Keywords: Autoregressive process; D-optimal chemical balance weighing design; Factorial design; Fischer’s inequality; Hadamard’s inequality (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:76:y:2013:i:3:p:393-407

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DOI: 10.1007/s00184-012-0394-8

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