Abstract
Minimax designs for logistic regression with one design variable are considered where the design space is a general interval [a, b] on the straight real line. This corresponds to a weighted linear regression model for a specific weight function. Torsney and López-Fidalgo (1995) computed maximum variance (MV-) optimal designs for simple linear regression for a general interval. López-Fidalgo et al. (1998) gave MV-optimal designs for symmetric weight functions and symmetric intervals, [-b, b]. Computations for general intervals for logistic regression are much more complex. Using similar approaches to these two papers and the equivalence theorem, explicit minimax optimal designs are given for different regions of points (a, b) in the semi-plane b>a for the logistic model. This complements Dette and Sahm (1998) who give a method for computing MV-optimal designs without any restriction on the design space. From this, Standardized Maximum Variance (SMV-) optimal designs immediately follow. The same approach could be used for probit, double exponential, double reciprocal and some other popular models in the biomedical sciences.
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References
Dette, H. (1997). Designing experiments with respect to `standardized’ optimality criteria.Journal of the Royal Statististical SocietyB59, 97–110.
Dette, H., Heiligers, B., and Studden, W.J. (1995). Minimax designs in linear regression models.The Annals of Statistics23, 30–40.
Dette, H. and Sahm, M. (1998). Minimax optimal designs in nonlinear regression models. StatisticaSinica8(4), 4249–4264.
Elfving, G. (1959). Design of linear experiments. In: Grenander, U. (ed.)Probability and Statistics. The Harald Cramür Volume.Almagrist and Wiksell, Stockholm, 58–74.
Fellman, J. (1974). On the allocation of linear observations.Soc. Sci. Fenn. Comment. Phys.Math., 44, 27–77.
Ford, I. (1976).Ph.D. Thesis.University of Glasgow.
Ford, I., Torsney, B., and Wu, C.F.J. (1992). The use of a canonical form in the construction of locally optimal designs for non-linear problems.Journal of the Royal Statistical SocietyB54, 569–583.
López-Fidalgo, J., Torsney, B., and Ardanuy, R. (1998).MV-optimization in weighted linear regression. In: Atkinson, A.C., Pronzato, L., and Wynn, H.P. (eds.)MODA 5- Advances in Model-OrientedData Analysis and Experimental Design.Springer-Verlag, New York, 39–50.
López-Fidalgo, J. and Wong, W.K. (2000). A comparative study of MV-and SMV-optimal designs for binary response models.Advances in Stochastic Simulation Methods386, 135–152.
Torsney, B. and López-Fidalgo J. (1995). MV-optimization in simple linear regression. In: Kitsos, C.P. and Müller, W.H. (eds.)MODA 5 - Advances in Model-Oriented Data Analysis. Springer-Verlag, New York, 57–69.
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Torsney, B., López-Fidalgo, J. (2001). Minimax Designs for Logistic Regression in a Compact Interval. In: Atkinson, A.C., Hackl, P., Müller, W.G. (eds) mODa 6 — Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57576-1_27
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DOI: https://doi.org/10.1007/978-3-642-57576-1_27
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1400-2
Online ISBN: 978-3-642-57576-1
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