Abstract
Two motivating examples are presented in order to appreciate the importance of optimal choice of covariates. Basics in linear models are discussed. Chapter-wise summary of the work covered and choice of various experimental design settings are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Late Professor Jack Kiefer pioneered the study of optimal experimental designs in standard ANOVA models as well as in regression designs. He guided Lopes Troya for her Doctoral Dissertation in a topic which was to bridge ANOVA and regression designs into what are known as ANCOVA models. The unfortunate premature death of Professor Kiefer was a blow to the design theorists in general. His expertise and insightful contributions could have gone a long way in this direction.
References
Chadjiconstantinidis S, Chadjipadelis T (1996) D-optimal cyclic complex linear designs and supplementary difference sets with association vector. J Stat Plan Inference 53:93–115
Chadjiconstantinidis S, Moyssiadis C (1991) Some D-optimal odd equi-eplicated designs for a covariate model. J Stat Plan Inference 28:83–93
Clatworthy WH (1973) Tables of two-associate class partially balanced designs. US Department of Commerce, National Bureau of Standards
Das K, Mandal NK, Sinha BK (2003) Optimal experimental designs with covariates. J Stat Plan Inference 115:273–285
Das P (2011) A review on optimum covariate designs. Calcutta Stat Assoc Bull, 63, 249–252. (Proceedings of the seventh international triennial calcutta symposium on probability statistics, December 28–31, 2009)
Dey A, Mukerjee R (2006) D-optimal designs for covariate models. Statistics 40:297–305
Dutta G (2004) Optimum choice of covariates in BIBD set-up. Calcutta Stat Assoc Bull 55:39–55
Dutta G (2009) Optimum designs for covariates models. (Unpublished Ph.D. Thesis)
Dutta G, Das P, Mandal NK (2007) Optimum choice of covariates for a series of SBIBDs obtained through projective geometry. J Mod Appl Stat Methods 6:649–656
Dutta G, Das P, Mandal NK (2009a) Optimum covariate designs in split-plot and strip-plot design set-ups. J Appl Stat 36:893–906
Dutta G, Das P, Mandal NK (2009b) Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups. J Stat Plan Inference 139:2823–2835
Dutta G, Das P, Mandal NK (2010a) Optimum covariate designs in binary proper equi-replicate block design set-up. Discret Math 310:1037–1049
Dutta G, Das P, Mandal NK (2010b) D-optimal Designs for covariate parameters in block design set-up. Commun Stat Theory Methods 39:3434–3443
Dutta G, Das P, Mandal NK (2010c) Tables for optimum covariate designs in PBIBD set-ups. J Indian Soc Agric Stat 64:375–389
Dutta G, Das P (2013a) Optimum design for estimation of regression parameters in multi-factor set-up. Commun Stat Theory Methods 42:4431–4443
Dutta G, Das P (2013b) Optimum designs for estimation of regression parameters in a balanced treatment incomplete block design set-up. J Stat Plan Inference 143:1203–1214
Dutta G, Das P, Mandal NK (2014) D-optimal designs for covariate models. Commun Stat Theory Methods 43:165–174
Dutta G, SahaRay R (2013) Optimal choice of covariates in the set-up of crossover designs. Stat Appl 11(1–2):93–109 (Special Issue in Memory of Professor M.N. Das)
Haggstrom GW (1975) Pitfalls Manpow Exp. RAND Corporation, Santa Monica
Harville DA (1974) Nearly optimal allocation of experimental units using observed covariate values. Technometrics 16:589–599
Harville, DA (1975) Computing optimum designs for covariate models. In: Srivastava JN (ed) A survey of statistical design and linear models. 209–228, Amsterdam, North Holland
Kurotschka V, Wierich W (1984) Optimale planung eines kovarianzanalyse und eines (Intraclass regressions experiments). Metrika 31:361–378
Liski EP, Mandal NK, Shah KR, Sinha BK (2002). Topics in optimal design. Lecture notes in statistics. Series 163, Springer, New York
Rao CR (1973) Linear statistical inference and its applications. 2nd edn, Wiley, USA
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
Scheffé H (1999) The analysis of variance. A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York
Shah KR, Sinha BK (1989) Theory of optimal designs. Lecture notes in statistics. Series 54, Springer, New York
Sinha BK (2009) A reflection on the choice of covariates in the planning of experimental designs. J Indian Soc Agric Stat 63:219–225
Snedecor GW, Cochran WG (1989) Stat Methods, 8th edn. Iowa State University Press, Ames, Iowa
Troya LJ (1982a) Optimal designs for covariate models. J Stat Plan Inference 6:373–419
Troya LJ (1982b) Cyclic designs for a covariate model. J Stat Plan Inference 7:49–75
Wierich W (1984) Konkrete optimale Versuchsplne fr ein lineares Modell mit einem qualitativen und zwei quantitativen Einflussfaktoren. Metrika 31:285–301
Wu CFJ (1981) Iterative construction of nearly balanced assignments I: Categorical covariates. Technometrics 23:37–44
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer India
About this chapter
Cite this chapter
Das, P., Dutta, G., Mandal, N.K., Sinha, B.K. (2015). Optimal Covariate Designs (OCDs): Scope of the Monograph. In: Optimal Covariate Designs. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2461-7_1
Download citation
DOI: https://doi.org/10.1007/978-81-322-2461-7_1
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2460-0
Online ISBN: 978-81-322-2461-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)