15 research outputs found
Robust T-optimal discriminating designs
This paper considers the problem of constructing optimal discriminating
experimental designs for competing regression models on the basis of the
T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975)
57-70]. T-optimal designs depend on unknown model parameters and it is
demonstrated that these designs are sensitive with respect to misspecification.
As a solution to this problem we propose a Bayesian and standardized maximin
approach to construct robust and efficient discriminating designs on the basis
of the T-optimality criterion. It is shown that the corresponding Bayesian and
standardized maximin optimality criteria are closely related to linear
optimality criteria. For the problem of discriminating between two polynomial
regression models which differ in the degree by two the robust T-optimal
discriminating designs can be found explicitly. The results are illustrated in
several examples.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1117 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
-optimal designs for discrimination between two polynomial models
This paper is devoted to the explicit construction of optimal designs for
discrimination between two polynomial regression models of degree and
. In a fundamental paper, Atkinson and Fedorov [Biometrika 62 (1975a)
57--70] proposed the -optimality criterion for this purpose. Recently,
Atkinson [MODA 9, Advances in Model-Oriented Design and Analysis (2010) 9--16]
determined -optimal designs for polynomials up to degree 6 numerically and
based on these results he conjectured that the support points of the optimal
design are cosines of the angles that divide half of the circle into equal
parts if the coefficient of in the polynomial of larger degree
vanishes. In the present paper we give a strong justification of the conjecture
and determine all -optimal designs explicitly for any degree
. In particular, we show that there exists a one-dimensional
class of -optimal designs. Moreover, we also present a generalization to the
case when the ratio between the coefficients of and is smaller
than a certain critical value. Because of the complexity of the optimization
problem, -optimal designs have only been determined numerically so far, and
this paper provides the first explicit solution of the -optimal design
problem since its introduction by Atkinson and Fedorov [Biometrika 62 (1975a)
57--70]. Finally, for the remaining cases (where the ratio of coefficients is
larger than the critical value), we propose a numerical procedure to calculate
the -optimal designs. The results are also illustrated in an example.Comment: Published in at http://dx.doi.org/10.1214/11-AOS956 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Optimal designs for estimating individual coefficients in polynomial regression with no intercept
In a seminal paper Studden (1968) characterized c-optimal designs in regression
models, where the regression functions form a Chebyshev system. He used these
results to determine the optimal design for estimating the individual coefficients in a
polynomial regression model on the interval [-1; 1] explicitly. In this note we identify
the optimal design for estimating the individual coefficients in a polynomial regression
model with no intercept (here the regression functions do not form a Chebyshev
system)