Abstract
This chapter addresses optimality issues for covariate designs under CRD set-up. We discuss optimum allocation of treatments and optimum selection of values of the covariates in this set-up for simultaneous estimation of the (fixed) treatment effects (in the absence of the general effect) and the covariate effects. We derive optimum designs for the most efficient estimation of treatment parameters and covariate parameters for finding such designs with respect to global optimality criterion. In cases where such designs do not exist, we take resort to D-optimality criterion.
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Das K, Mandal NK, Sinha BK (2003) Optimal experimental designs with covariates. J Stat Plan Inference 115:273–285
Dey A, Mukerjee R (2006) D-optimal designs for covariate models. Statistics 40:297–305
Dutta G, Das P, Mandal NK (2014) D-Optimal designs for covariate models. Commun Stat Theory Methods 43:165–174
Galil Z, Kiefer J (1980) D-optimum weighing designs. Ann Stat 8:1293–1306
Hedayat AS, Sloane NJA, Stufken J (1999) Orthogonal arrays: theory and applications. Springer, New York
Pukelsheim F (1993) Optimal design of experiments. Wiley, New York
Rao CR (1973) Linear statistical inference and its applications. Wiley, New York
Rao PSSNVP, Rao SB, Saha GM, Sinha BK (2003) Optimal designs for covariates’ models and mixed orthogonal arrays. Electron Notes Discret Math 15:157–160
Shah KR, Sinha BK (1989) Theory of optimal designs. lecture notes in statistics, Series 54. Springer, New York
Troya Lopes J (1982a) Optimal designs for covariate models. J Stat Plan Inference 6:373–419
Troya Lopes J (1982b) Cyclic designs for a covariate model. J Stat Plan Inference 7:49–75
Wojtas M (1964) On Hadamard’s inequality for the determinants of order non-divisible by 4. Colloq Math 12:73–83
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© 2015 Springer India
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Das, P., Dutta, G., Mandal, N.K., Sinha, B.K. (2015). OCDs in Completely Randomized Design Set-Up. In: Optimal Covariate Designs. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2461-7_2
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DOI: https://doi.org/10.1007/978-81-322-2461-7_2
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Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2460-0
Online ISBN: 978-81-322-2461-7
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