Abstract
Some optimal statistical properties of C-designs in certain nested block designs under a mixed model are characterized.
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References
Bagchi, S. (1987a). On the E-optimality of certain asymetrical designs under mixed effects model. Metrika 37, 95–105.
Bagchi, S. (1987b). On the optimalities of the MBGDDs under mixed effects model. Report, Computer Science Unit, Indian Statistical Institute, Calcutta, India.
Banerjee, S. and Kageyama, S. (1990). Existence of a-resolvable nested incomplete block designs. Utilitas Math. 38, 237–243.
Banerjee, S. and Kageyama, S. (1993). Methods of constructing nested partially balanced incomplete block designs. Utilitas Math. 43, 3–6.
Bogacka, B. and Mejza, S. (1993). On BU-optimality of block designs under mixed model. Bulletin of the International Statistical Institute, Contributed Papers, Book 1, 139–140.
Bogacka, B. and Mejza, S. (1994). Optimality of generally balanced experimental block designs. Proc. of the International Conference on Linear Statistical Inference, LINS TAT 93, T.Caliriski and R.Kala, eds, Kluwer Academic Publishers, Dordrecht, 185–194.
Bondar, J. V. (1983). Universal optimality of experimental designs: definitions and a criterion. Canad. J. Statist. 11, 325–331.
Bose, R. C. (1942). A note on the resolvability of balanced incomplete block designs. Sankhyâ 6, 105–110.
Calinski, T. (1977). On the notion of balance in block designs. In: J. R. Barra, F. Brodeau, G. Romier and B. van Cutsem, Eds., Recent Developments in Statistics. North-Holland, Amsterdam, 365–374.
Ceranka, B., Kageyama, S. and Mejza, S. (1986). A new class of C-designs. Sankhyâ B 48, 199–206.
Cheng, C. S. (1978). Optimality of certain asymetrical experimental designs. Ann. Statist. 6, 1239–1261.
Dey, A., Das, U. S. and Banerjee, A. K. (1986). Constructions of nested balanced incomplete block designs. Calcutta Statist. Assoc. Bull. 35, 161–167.
Hormel, R. J. and Robinson, J. (1975). Nested partially balanced incomplete block designs. Sankhyâ B 37, 201–210.
Houtman, A. M. and Speed, T. P. (1983). Balance in designed experiments with orthogonal block structure. Ann. Statist. 11, 1069–1085.
Jacroux, M. (1989). On the E-optimality of block designs under the assumption of random block effects. Sankhyâ B 51, 1–12.
Jimbo, M. and Kuriki, S. (1983). Constructions of nested designs. Ars Combin. 16, 275–285.
John, J. A. and Mitchell, T. J. (1977). Optimal incomplete block designs. J. Roy. Statist. Soc. B 39, 39–43.
Kageyama, S. (1973). On p-resolvable and affine p-resolvable balanced incomplete block designs. Ann. Statist. 1, 195–203.
Kageyama, S. (1980). On properties of efficiency-balanced designs. Commun. Statist. A 9, 597–616.
Kageyama, S. (1984). Some properties on resolvability of variance-balanced designs. Geom. Dedicata 15, 289–292.
Khatri, C. G. and Shah, K. R. (1984). Optimality of block designs. In: Proc. Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions, Calcutta, 326–332.
Kiefer, J. (1975). Construction and optimality of generalized Youden designs. In: J. N. Srivastava, Ed., A Survey of Statistical Design and Linear Models. North-Holland, Amsterdam, 333–353.
Mejza, S. (1992). On some aspects of general balance in designed experiments. Statistica 2, 263–278.
Mukerjee, R. and Kageyama, S. (1985). On resolvable and affine resolvable variance-balanced designs. Biometrika 72, 165–172.
Mukhopadhyay, S. (1981). On the optimality of block designs under mixed effects model. Calcutta Statist. Assoc. Bull. 30, 171–185.
Nelder, J. A. (1965). The analysis of randomized experiments with orthogonal block structure. Block structure and the null analysis of variance. Proc. Roy. Soc. London A 283, 147–178.
Nigam, A. K., Puri, P. D. and Gupta, V. K. (1988). Characterizations and Analysis of Block Designs. Wiley Eastern, New Delhi.
Patterson, H. D. and Williams, E. R. (1976). A new class of resolvable incomplete block designs. Biometrika 63, 83–92.
Preece, D. A. (1967). Nested balanced incomplete block designs. Biometrika 54, 479–486.
Saha, G. M. (1976). On Calinskis patterns in block designs. Sankhyâ B 38, 383–392.
Shah, K. R. and Sinha, B. K. (1989). Theory of Optimal Designs. Springer-Verlag, Berlin.
Shrikhande, S. S. and Raghavarao, D. (1964). Affine a-resolvable incomplete block designs. Contributions to Statistics (edited by C. R. Rao), pp. 471–480. Pergamon Press, Statistical Publishing Society, Calcutta.
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Mejza, S., Kageyama, S. (1995). On the Optimality of Certain Nested Block Designs under a Mixed Effects Model. In: Kitsos, C.P., Müller, W.G. (eds) MODA4 — Advances in Model-Oriented Data Analysis. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12516-8_17
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DOI: https://doi.org/10.1007/978-3-662-12516-8_17
Publisher Name: Physica, Heidelberg
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