Minimax Designs in Linear Regression Models
نویسندگان
چکیده
منابع مشابه
Minimax Regression Designs for Approximately Linear Models with Autocorrelated Errors
We study the construction of regression designs, when the random errors are autocorrelated. Our model of dependence assumes that the spectral density g(~o) of the error process is of the form g ( o ) = (1 -a)go(~O ) + ~gl(o), where go(CO) is uniform (corresponding to uncorrelated errors), ct ~ [0, 1) is fixed, and gx(to) is arbitrary. We consider regression responses which are exactly, or only ...
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We consider the approximately linear regression model E b 1x1 = I(x) 0 + f(x), XE S, where f(x) is a non-linear disturbance restricted only by a bound on its &(S) norm, and where S is the design space. For loss functions which are monotonic functions of the mean squared error matrix, we derive a theory to guide in the construction of designs which minimize the maximum (over f) loss. We then spe...
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The authors propose and explore new regression designs. Within a particular parametric class, these designs are minimax robust against bias caused by model misspecification while attaining reasonable levels of efficiency as well. The introduction of this restricted class of designs is motivated by a desire to avoid the mathematical and numerical intractability found in the unrestricted minimax ...
متن کاملExistence and symmetry of minimax regression designs
In this paper we address two important issues about minimax regression designs: existence and symmetry. These designs are robust against possible misspecification of the regression response. Existence is proved for A-optimal, D-optimal and Q-optimal minimax designs. Symmetry is proved for all D-optimal minimax designs and for some special cases of A-optimal and Q-optimal minimax designs.
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1995
ISSN: 0090-5364
DOI: 10.1214/aos/1176324453