A weighted geometric regularity from order restricted statistical inference |
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Authors: | Chul Gyu Park Sangwook Ree |
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Institution: | (1) School of Education, University of Cincinnati, P.O. Box 210049, Cincinnati, OH 45221, USA |
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Abstract: | In Euclideank-space, the cone of vectors x = (x 1,x 2,...,x k ) satisfyingx 1 ≤x 2 ≤ ... ≤x k and $\sum\nolimits_{j = 1}^k {x_j } = 0$ is generated by the vectorsv j = (j ?k, ...,j ?k,j, ...,j) havingj ?k’s in its firstj coordinates andj’s for the remainingk ?j coordinates, for 1 ≤j <k. In this equal weights case, the average angle between v i and v j over all pairs (i, j) with 1 ≤i <j <k is known to be 60°. This paper generalizes the problem by considering arbitrary weights with permutations. |
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