Nonparametric estimation for dependent data

Abstract

In this paper, we consider nonparametric estimation for dependent data, where the observations do not necessarily come from a linear process. We study density estimation and also discuss associated problems in nonparametric regression, using the 2-mixing dependence measure. We compare the results under the 2-mixing with those derived under the assumption that the process is linear.

Keywords:

• density estimation
• nonparametric regression
• 2-mixing
• nonlinear processes

AMS Subject Classification:

• Primary: 62G05
• 62M10
• Secondary: 62G07
• 62G08

Acknowledgements

The authors are grateful to Rainer Dahlhaus, Rafal Kulik and two anonymous referees for making several useful suggestions. This work has been partially supported by the DFG (DA 187/12-3), the IAP research network no. P6/03 of the Belgian Government (Belgian Science Policy) and the NSF grant DMS-0806096.

Notes

We use the notation and .