On D-Optimality Criterion of Non-Overlapping and Overlapping Segmentation of the Response Surfaces

T.A. Ugbe ； P.E Chigbu

《Research Journal of Mathematics and Statistics》 4卷1期 (2012/02) Pp. 1-5

並列摘要

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.

並列關鍵字

Design matrix ； determinant ； information matrix ； optimality ； segmentation ； support points