Partially linear models on Riemannian manifolds

In partially linear models the dependence of the response y on (x^T,t) is modeled through the relationship y=\x^T β+g(t)+ε where εis independent of (x^T,t). In this paper, estimators of βand g are constructed when the explanatory variables t take values on a Riemannian manifold. Our proposal combine the flexibility of these models with the complex structure of a set of explanatory variables. We prove that the resulting estimator of βis asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators. Finally, we applied the studied model to an example based on real dataset.

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