Abstract
The robustness of block designs against missing observations is revisited. It has been shown that A-efficiency criterion is not an appropriate measure to judge the efficiency of the residual design. As an alternate to this, E-efficiency criterion is defined. A lower bound of this criterion for the loss of any t observations in binary variance balanced block design is obtained. Balanced incomplete block designs (BIBD) that are robust as per E-efficiency criterion are identified.
Similar content being viewed by others
References
Baksalary, J.K. and Tabis, Z. (1987). Conditions for the robustness of block designs against the unavailability of data. J. Statist. Plann. Inference, 16, 49–54.
Bhar, L. and Gupta, V.K. (2002). Robust row-column designs for complete diallel cross experiments. Metrika, 56, 83–90.
Das A. and Kageyama, S. (1992). Robustness of BIB and extended BIB designs against the nonavailability of any number of observations in a block. Comput. Statist. Data Anal., 14, 343–358.
Dey, A. (1993). Robustness of block designs against missing data. Statist. Sinica, 3, 219–231.
Dey, A., Chand, K.M. and Buchthal, D.C. (1996). Efficiency of the residual design under the loss of observations in a block. J. Ind. Soc. Agril. Statist., 49, 237–249.
Duan, X. and Kageyama, S. (1995). Robustness of augmented BIB designs against the unavailability of some observations. Sankhya, B57, 405–419.
Ghosh, S. (1979). On robustness of designs against incomplete data. Sankhya, B40, 204–208.
Ghosh, S. (1982). Robustness of BIBD against the unavailability of data. J. Statist. Plann. Inference, 6, 29–32.
Godolphin, J.D. and Warren, H.R. (2011). Improved conditions for the robustness of binary block designs against the loss of whole blocks. J. Statist. Plann. Inference, 141, 3498–3505.
Jacroux, M. (1989). On the E-optimality of block designs under the assumption of random block effects. Sankhya, B51, 1–12.
Kageyama, S. (1990). Robustness of Block Designs. In Probability Statistics and Design of Experiments (R. R. Bahadur, ed.). Wiley Eastern, New Delhi, pp. 425–438.
Kiefer, J. (1958). On the nonrandomized optimality and randomized optimality of symmetrical designs. Ann. Math. Statist., 29, 675–699.
Lal, K., Gupta, V.K. and Bhar, L. (2001). Robustness of designed experiments against missing data. J. Appl. Stat., 28, 63–79.
Morgan, J.P. and Parvu, V. (2008). Most robust BIBDs. Statist. Sinica, 18, 689–707.
Mukerjee, R. and Kageyama, S. (1990). Robustness of group divisible designs. Commun. Statist. – Theo. Meth., 19, 3189–3203.
Parsad, R., Gupta, V.K., Khanduri, O.P. (2000). Cataloguing and construction of variance balanced block designs: Computer algorithms for construction. Technical Report. Indian Agricultural Statistics Research Institute, New Delhi. (Catalogue of BIB design for r <=30 for symmetric and r <=20 for asymmetric data, Design Resources Server. Indian Agricultural Statistics Research Institute (ICAR), New Delhi 110 012, India. www.iasri.res.in/design.)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bhar, L. Robustness of Variance Balanced Block Designs. Sankhya B 76, 305–316 (2014). https://doi.org/10.1007/s13571-013-0073-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13571-013-0073-4