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Abstract
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Article Information:
On D-Optimality Criterion of Non-Overlapping and Overlapping Segmentation of the Response Surfaces
T.A. Ugbe and P.E Chigbu
Corresponding Author: T.A. Ugbe
Submitted: 2011 October, 12
Accepted: 2011 November, 18
Published: 2012 February, 25 |
Abstract:
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The aim of this study was to find out the Segment which generates a design that is D-optimal(has
minimum variance). This was achieved by partitioning the Response Surface into two equal segments for Nonoverlapping
and Overlapping Segments and then select support points which formed the design matrices for
the segments. Further more, the determinant of the information Matrices of the designs were compared for both
Non-overlapping and Overlapping Segments using the Unbiased response function and the biased response
function respectively. It was found that design 1 is D-optimal and also G-optimal (by equivalence theorem
given in theorem 1),that is the Non-Overlapping Segmentation of the Response Surface forms a design which
is D- and G-optimal for the first order unbiased response function and second order biased response function,
respectively. In other words, the Overlapping Segmentation of the Response Surfaces form a design that was
not D-optimal.
Key words: Design matrix, determinant, information matrix, optimality, segmentation, support points,
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Cite this Reference:
T.A. Ugbe and P.E Chigbu, . On D-Optimality Criterion of Non-Overlapping and Overlapping Segmentation of the Response Surfaces. Research Journal of Mathematics and Statistics, (1): 1-5.
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ISSN (Online): 2040-7505
ISSN (Print): 2042-2024 |
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