Spacing of information in polynomial regression:a simple solution |
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Authors: | Luis A Escobar James L Cornette |
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Institution: | 1. Experimental Statistics , Louisiana State University , Baton Rouge , Louisiana , 70803;2. Department of Mathematics , Iowa State University , Ames , Iowa , 50011 |
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Abstract: | Consider a k polynomial regression on a single real variable. If n uncorrelated observations are to be taken in a design with support on more than k+1 points, there is an approximate experiment, ν, with support on k+1 points and n observations such that both designs have the same information matrix for the model. A proof of this result is provided. A method to obtain the approximate design ν is given and illustrated by an example. The source of disagreement between Kiefer (1959) and De La Garza (1954) in the solution of this problem is clarified. |
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Keywords: | approximate design exact design information matrix problem of moments |
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