Construction of optimal designs using a clustering approach

There are a variety of problems in statistics which require the calculation of one or several optimizing probability distributions or measures. A class of multiplicative algorithms, indexed by functions f ( . ) of derivatives is considered. The performance of the algorithm is first investigated in f...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2006-03, Vol.136 (3), p.1120-1134
Main Authors: Mandal, S., Torsney, B.
Format: Article
Language:English
Subjects:
Clustering approach
Clusters
Directional derivatives
Multiplicative algorithms
Optimal design
Optimality conditions
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Summary:There are a variety of problems in statistics which require the calculation of one or several optimizing probability distributions or measures. A class of multiplicative algorithms, indexed by functions f ( . ) of derivatives is considered. The performance of the algorithm is first investigated in finding one optimizing distribution, namely a D-optimal design on a continuous compact (design) interval or space. In practice we must discretize these spaces. The optimum design often turns out to be a distribution defined on disjoint clusters of points. These clusters begin to ‘form’ early on in the above iterations. The idea is that, at an appropriate iterate p ( r ) , the single distribution p ( r ) should be replaced by conditional distributions within clusters and a marginal distribution across the clusters. This approach is formulated for a general regression model and, then is explored through several regression models. Considerable improvements in convergence are seen for each of these models.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2004.08.005