Tensor Product Space ANOVA Fits to Incomplete Unbalanced Discrete Multi-way Layouts
نویسنده
چکیده
The discrete multi-way layout is a widespread data-type associated with experimental designs, gene or protein chips, digital images or videos, and more. A discrete multi-way layout has a finite number of factor level combinations. The layout may be unbalanced or incomplete or both. We consider candidate fits to an incomplete layout that are least squares fits to certain submodels induced by tensor product space ANOVA models for a complete layout. The candidate estimator with smallest estimated risk is defined to be the regularized fit. Stable algorithms for the Moore-Penrose inverse provide a way to compute it. Multiparametric asymptotics under a Gaussian model show that the limiting risk of a regularized fit can be much smaller than that of the usual least squares fit to the incomplete multi-way layout. Case studies make evident the benefits of such theoretically small risk.
منابع مشابه
Low Risk Fits to Discrete Incomplete Multi-way Layouts
The discrete multi-way layout is a widespread data-type associated with regression, experimental designs, gene or protein chips, digital images or videos, and more. A discrete multi-way layout has a finite number of factor level combinations. The layout may be unbalanced or incomplete or both. We consider candidate fits to an incomplete layout that are least squares fits to certain submodels in...
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