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Minimum variance rectangular designs for U-statistics |
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| Authors: | Grzegorz A. Rempala Sudesh Srivastav |
| Affiliation: | a Department of Mathematics, University of Louisville, Louisville, KY 40292, USA b Department of Biostatistics, Tulane University, USA |
| Abstract: | We consider a certain class of rectangular designs for incomplete U-statistics based on Latin squares and show it to be optimal with respect to the minimal variance criterion. We also show it to be asymptotically efficient when compared with the corresponding complete statistics, as well as uniformly more efficient than the random subset selection. We provide the necessary and sufficient conditions for the existence of our design and give some examples of applications. |
| Keywords: | Incomplete U-statistic Partially balanced design Minimum variance criterion Latin square Asymptotic efficiency Rectangular association scheme |
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