Abstract
The aim of this paper is to consider the optimality in the growth curve model with respect to two aspects: time and the block design and to show some relations between information functions for different designs. The A-, D- and E- optimality are studied.
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Abt M, Gaffke N, Liski EP, Sinha BK (1998) Optimal designs in growth curve models-II, correlated model for quadratic growth: optimal designs for parameter estimation and growth prediction. J Stat Plan Inference 67: 287–296
Azais J-M, Bailey RA, Mond H (1993) The consultant’s forum. A catalogue of efficient neighbour—design with boder plots. Biometrics 49: 1252–1261
Caliński T, Kageyama S (2000) Block designs: a randomization approach, vol I. Springer-Verlag, New York
Chang F-C, Lay C-F (2002) Optimal designs for growth curve models. J Stat Plan Inference 104: 427–438
Cheng C-S (1978) Optimality of certain asymmetrical experimental designs. Ann Stat 6(6): 1239–1261
Cheng C-S (1980) On the E-optimality of some block design. J R Stat Soc B 42(2): 199–204
de la Garza A (1954) Spacing of information in polynomial regression. Ann Math Stat 25: 123–130
Filipiak K, Markiewicz A, Szczepańska A (2009) Optimal designs under a multivariate linear model with additional nuisance parameters. Stat Papers 50: 761–778
Filipiak K, Szczepańska A (2005) A-, D- and E-optimal designs for quadratic and cubic growth curve models with correlated errors. Biom Lett 42/1: 43–56
Filipiak K, Szczepańska A (2007) A-optimal designs under a quadratic growth curve model in the transformed time interval. Biom Lett 44/2: 85–96
Gaffke N (1982) D-optimal block designs with at most six varieties. J Stat Plan Inference 6: 183–200
Gaffke N, Heiligers B (1998) Minimum support invariant design for multiple cubic regression. J Stat Plan Inference 72: 229–245
Hedayat A, Li S-Y (1979) The trade-off method in the construction of BIB designs with variable support size. Ann Stat 7(6): 1277–1287
Imhof LA (1998) A-optimum extract design for quadratic regresion. J Math Anal Appl 228: 157–165
John JA (1987) Cyclic designs. Chapman and Hall, New York
Luoma A, Mandal NK, Sinha BK (2001) A-optimal cubic and quartic regression designs in asymmetric factor spaces. Stat Appl 3: 147–153
Majumar D, Notz WI (1983) Optimal incomplete block design for comparing treatments with a control. Ann Stat 11(1): 258–266
Mandal NK (2002) Optimal regression design in symmetric domains. Design workshop lecture notes. ISI, Kolkata, pp 23–32
Markiewicz A, Szczepańska A (2007) Optimal designs for multivariate linear models. Stat Probab Lett 77: 426–430
Moerbeek M (2005) Robustness properties of A-, D-, and E-optimal designs for polynomial growth models with autocorrelated errors. Comput Stat Data Anal 48: 765–778
Potthoff RF, Roy SN (1964) A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 51: 313–326
Pukelsheim F (1993) Optimal designs of experiments. Wiley, New York
Schott JR (1997) Analysis for statistics. Wiley, Toronto
Srivastav SK, Shankar A (2003) On the E-optimality of certain class of block design. Stat Probab Lett 65: 187–193
Yang M (2010) On the de la Garza phenomenon. Ann Stat 38: 2499–2524
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The author would like to thank the referees for valuable comments and suggestions.
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Szczepańska, A. Simultaneous choice of time points and the block design in the growth curve model. Stat Papers 54, 413–425 (2013). https://doi.org/10.1007/s00362-012-0438-1
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DOI: https://doi.org/10.1007/s00362-012-0438-1