Partially linear models on Riemannian manifolds

WENCESLAO GONZALEZ MANTEIGA; GUILLERMO HENRY; DANIELA RODRIGUEZ

JOURNAL OF APPLIED STATISTICS

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD

Año: 2012 vol. 83 p. 203 - 2012

0266-4763

In partly linear models, the dependence of the response $y$ on $(x^{ ras},t)$ is modeled through the relationship $ y=x^{ ras} beta+g(t)+arepsilon$ where $arepsilon$ is independent of ?$(x^{ ras},t)$. In this paper, estimators of $beta$ and $g$ 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 the explanatory variables. We show that the proposed estimator is asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators and we applied the studied model to an environment dataset.