Stochastic Design Criteria in Linear Models
DOI:
https://doi.org/10.17713/ajs.v34i2.413Abstract
Within the framework of classical linear regression model stochastic optimal design criteria are considered. As examples a line fit model and a k-way linear fit model are taken. If the optimal design does not exist, an approach consisting in choosing the efficient design is suggested.
References
A. De la Garza. Spacing of information in polynomial estimation. Ann. Math. Stat., 25:123–130, 1954.
K.-H. Li and N.N. Chan. Lp-optimality for regression designs under correlations. Stat. Sinica, 12:1015–1026, 2002.
E.P. Liski, A. Luoma, and A. Zaigraev. Distance optimality design criterion in linear models. Metrika, 49:193–211, 1999.
E.P. Liski, N.K. Mandal, K.R. Shah, and B.K. Sinha. Topics in Optimal Design. Lecture Notes in Statistics, 163, Springer-Verlag, New York, 2002.
E.P. Liski and A. Zaigraev. A stochastic characterization of Loewner optimality design criterion in linear models. Metrika, 53:207–222, 2001.
A.W. Marshall and I. Olkin. Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979.
F. Pukeslheim. Optimal Design of Experiments, Wiley, New York, 1993.
C.R. Rao. Linear Statistical Inference and Its Applications, Wiley, New York, 2nd edition, 1973.
J.M. Rodrigues-Diaz and J. López-Fidalgo. A bi-dimensional class of optimality criteria involving ϕ_p and characteristic criteria. Statistics, 37(4):325–334, 2003.
B.K. Sinha. On the optimality of some design. Calcutta Statistical Association Bulletin, 20:1–20, 1970.
A. Zaigraev. Shape optimal design criterion in linear models. Metrika, 56:259–273, 2002.
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