Wavelet-based estimators of multivariable mean regression function with long-memory data

ABSTRACT

Wavelet analysis has been proved to be a powerful statistical technique in the non parametric regression. In this paper, we propose non linear wavelet-based estimators for multivariable mean regression function with long-memory data. We also provide an asymptotic expansion for the mean integrated squared error (MISE) of the function estimators. This MISE expansion still works even when the underlying mean regression function is only piecewise smooth. This paper extends the corresponding results in the literature for single variable to multivariable case.

KEYWORDS:

• Long-range dependence
• mean integrated squared error
• multivariable non parametric regression
• non linear wavelet-based estimator
• piecewise smooth.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62G20

Acknowledgments

The authors would like to sincerely thank two referees for their constructive comments and suggestions, which have greatly improved the manuscript.