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Z. Galil

Bio: Z. Galil is an academic researcher from Cornell University. The author has contributed to research in topics: Polynomial regression & Optimal design. The author has an hindex of 1, co-authored 1 publications receiving 63 citations.

Papers
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Journal ArticleDOI
Z. Galil1, J. Kiefer1
TL;DR: In this paper, the authors considered quadratic regression with mixtures of nonnegative components and compared the designs that are optimum with respect to the D-, A-, and E-optimality criteria in their performance relative to these and other criteria.
Abstract: Designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x 1, x 2, …, x q + 1) of nonnegative components x i with Σ q + 1 1 x i = 1. The designs that are optimum with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except when q = 2, the A-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously known D-optimum design. Although the E-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.

64 citations


Cited by
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Journal ArticleDOI
TL;DR: An overview and critical analysis of the state of the art in this sector are proposed and the main contributions to model-based experiment design procedures in terms of novel criteria, mathematical formulations and numerical implementations are highlighted.

650 citations

Journal ArticleDOI
TL;DR: The practical importance of qualitative experiment design is illustrated by a very simple biological model, and special emphasis is given to methods allowing uncertainty on the prior information to be taken into account.

299 citations

Book
10 Apr 2013
TL;DR: In this article, asymptotic designs and uniform convergence of LS estimators are discussed. But the authors focus on the small-sample precision of the LS estimator, not on the optimality of the estimator itself.
Abstract: Introduction.- Asymptotic designs and uniform convergence. Asymptotic properties of the LS estimator.- Asymptotic properties of M, ML and maximum a posteriori estimators.- Local optimality criteria based on asymptotic normality.- Criteria based on the small-sample precision of the LS estimator.- Identifiability, estimability and extended optimality criteria.- Nonlocal optimum design.- Algorithms-a survey.- Subdifferentials and subgradients.- Computation of derivatives through sensitivity functions.- Proofs.- Symbols and notation.- List of labeled assumptions.- References.

132 citations

Journal ArticleDOI
TL;DR: In this paper, an alternative representation for mixtures of ingredients is discussed which offers attractive symmetries, compact notation and homogeneous model functions based on the Kronecker algebra of vectors and matrices, used successfully in previous response surface work.

82 citations