Robust Estimators in Partly Linear Regression Models on Riemannian Manifolds

abstract

Under a partly linear model we study a family of robust estimates for the regression parameter and the regression function when some of the predictors take values on a Riemannian manifold. We obtain the consistency and the asymptotic normality of the proposed estimators. Simulations and an application to a real data set show the good performance of our proposal under small samples and contamination .

Keywords:

• Non parametric estimation
• Partly linear models
• Riemannian manifolds
• Robustness

Acknowledgments

We wish to thank the two anonymous referees for valuable comments which led to an improved version of the original paper.

Additional information

Funding

This research was partially supported by Grants 20020100300057 from the Universidad de Buenos Aires, PIP 1122008010216 from CONICET, and PICT–00821 from ANPCYT, Argentina.