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Abstract:
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In this talk, we consider an estimation problem in a generalized tensor regression model with multi-mode covariates. We generalize the main results in recent literature in five ways. First, the dependence structure of the error and covariates are as weak as an L2-mixingale array, and the error term does not need to be uncorrelated with regressors. Second, we consider a more general constraint than the one considered in previous works. Third, we derive the joint asymptotic distribution of the unrestricted tensor estimator (UE) and restricted tensor estimator (RE). Fourth, we propose a class of shrinkage-type estimators in the context of tensor regression and under some concave loss functions, we derive the asymptotic distributional risk (ADR). Fifth, we derive sufficient conditions for which the shrinkage estimators dominate the UE. In addition to these interesting contributions, we derive some identities which are useful in studying the risk dominance of shrinkage-type tensor estimators. Finally, to illustrate the application of the proposed methods, we corroborate the results by some simulation studies of binary, Normal and Poisson data and we analyze some neuro-imaging datasets.
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