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We propose a novel broadcasting idea to model the nonlinearity in tensor regression non-parametrically. Unlike existing non-parametric tensor regression models, the resulting model strikes a good balance between flexibility and interpretability. A penalized estimation and corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation enjoys a desirable convergence rate. We also provide a minimax lower bound, which characterizes the optimality of the proposed estimator in a wide range of scenarios. Numerical experiments are conducted to confirm the theoretical finding and show that the proposed model has advantages over existing linear counterparts.
In many applications there is interest in estimating the relation between a predictor and an outcome when the relation is known to be monotone or otherwise constrained due to the physical processes involved. We consider one such application--inferrin
A simple Bayesian approach to nonparametric regression is described using fuzzy sets and membership functions. Membership functions are interpreted as likelihood functions for the unknown regression function, so that with the help of a reference prio
One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We propose a Gaussi
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Many time-to-event studies are complicated by the presence of competing risks. Such data are often analyzed using Cox models for the cause specific hazard function or Fine-Gray models for the subdistribution hazard. In practice regression relationshi