We consider the design of experiments when estimation is to be performed using locally weighted regression methods. We adopt criteria that consider both estimation error (variance) and error resulting from model missp...
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We consider the design of experiments when estimation is to be performed using locally weighted regression methods. We adopt criteria that consider both estimation error (variance) and error resulting from model misspecification (bias). Working with continuous designs, we use the ideas developed in convex design theory to analyze properties of the corresponding optimal designs. Numerical procedures for constructing optimal designs are developed and applied to a variety of design scenarios in one and two dimensions. Among the interesting properties of the constructed designs are the following: (1) Design points tend to be more spread throughout the design space than in the classical case. (2) The optimal designs appear to be less model and criterion dependent than their classical counterparts. (3) While the optimal designs are relatively insensitive to the specification of the design space boundaries, the allocation of supporting points is strongly governed by the points of interest and the selected weight function, if the latter is concentrated in areas significantly smaller than the design region. Some singular and unstable situations occur in the case of saturated designs. The corresponding phenomenon is discussed using a univariate linear regression example. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper we present two new concepts related to the solution of systems of nonsmooth equations (NE) and variational inequalities (VI). The first concept is that of a normal merit function, which summarizes the si...
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In this paper we present two new concepts related to the solution of systems of nonsmooth equations (NE) and variational inequalities (VI). The first concept is that of a normal merit function, which summarizes the simple basic properties shared by various known merit functions. In general, normal merit functions are locally Lipschitz, but not differentiable. The second concept is that of a Newtonian operator, whose values generalize the concept of the Hessian for normal merit functions. These two concepts are then used to generalize the nonsmooth Newton method for solving the equation del f(x) = 0, where f is a normal merit function with f is an element of C-1, to the case where f is only locally Lipschitz and the set-valued inclusion 0 is an element of partial derivative f(x) needs to be solved. Combining the resulting generalized Newton method with certain first-order methods, we obtain a globally and superlinearly convergent algorithm for minimizing normal merit functions.
A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed...
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A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator design problem with a band of excitation frequencies.
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