A robust and efficient estimation method for nonparametric models with jump points

ABSTRACT

Nonparametric models with jump points have been considered by many researchers. However, most existing methods based on least squares or likelihood are sensitive when there are outliers or the error distribution is heavy tailed. In this article, a local piecewise-modal method is proposed to estimate the regression function with jump points in nonparametric models, and a piecewise-modal EM algorithm is introduced to estimate the proposed estimator. Under some regular conditions, the large-sample theory is established for the proposed estimators. Several simulations are presented to evaluate the performances of the proposed method, which shows that the proposed estimator is more efficient than the local piecewise-polynomial regression estimator in the presence of outliers or heavy tail error distribution. What is more, the proposed procedure is asymptotically equivalent to the local piecewise-polynomial regression estimator under the assumption that the error distribution is a Gaussian distribution. The proposed method is further illustrated via the sea-level pressures.

KEYWORDS:

• EM algorithm
• Jump-preserving curve fitting
• Local piecewise-modal regression
• Nonparametric regression

Funding

This work is partly supported by the Natural Science Research Foundation of China (11571073, 11401094, 11301073), Jiangsu Provincial Natural Science Foundation in China (BK20141326), and the Research Fund for the Doctoral Program of Higher Education of China (20120092110021), the Social Science Fund of the Ministry of Education under Grant 13YJC910006.