Constructing optimal designs with constraints

Mandal, Saumen; Torsney, Ben; Carrière, Keumhee C.

doi:10.1016/j.jspi.2003.12.003

Cited by 12 publications

(11 citation statements)

References 12 publications

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“…For related discussion of this algorithm, see Torsney (), Silvey, Titterington & Torsney (), Titterington (), Mandal & Torsney (), Torsney & Mandal (), Torsney & Alahmadi (), and Mandal et al . (). For further developments based on clustering, see Mandal & Torsney ().…”

Section: Algorithmsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

“…Mandal et al . () and Torsney & Mandal () constructed optimal designs by maximising a standard criterion subject to the constraint of zero covariance of the estimators of parameters of interest. They solved this constrained optimisation problem by a Lagrangian method.…”

Section: Introductionmentioning

confidence: 99%

“…This problem is an example of optimal regression design in which we need to calculate an optimising probability distribution. Some previous work in this direction includes Mandal, Torsney & Carriere (2005), Torsney & Mandal (2001), and Torsney & Alahmadi (1995). Mandal et al (2005) and Torsney & Mandal (2001) constructed optimal designs by maximising a standard criterion subject to the constraint of zero covariance of the estimators of parameters of interest.…”

Section: Introductionmentioning

confidence: 99%

“…The contribution of the present work, and the differences between it and the references cited above, are as follows. In contrast with the work of Mandal et al (2005) and Torsney & Mandal (2001), the present work is based directly on optimising covariances without considering a standard optimality criterion such as D or A-optimality. In contrast with the work of Torsney & Alahmadi (1995), we formulate the criterion as a general function of the weights and do not need to consider the signs of the coefficients.…”

Section: Introductionmentioning

confidence: 99%

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Optimal designs for minimising covariances among parameter estimators in a linear model

Mandal

Torsney

Chowdhury

2017

Aus NZ J of Statistics

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Summary We construct approximate optimal designs for minimising absolute covariances between least‐squares estimators of the parameters (or linear functions of the parameters) of a linear model, thereby rendering relevant parameter estimators approximately uncorrelated with each other. In particular, we consider first the case of the covariance between two linear combinations. We also consider the case of two such covariances. For this we first set up a compound optimisation problem which we transform to one of maximising two functions of the design weights simultaneously. The approaches are formulated for a general regression model and are explored through some examples including one practical problem arising in chemistry.

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