The kernel regression estimation for randomly censored functional stationary ergodic data

ABSTRACT

In this paper, we investigate the asymptotic properties of the kernel estimator for non parametric regression operator when the functional stationary ergodic data with randomly censorship are considered. More precisely, we introduce the kernel-type estimator of the non parametric regression operator with the responses randomly censored and obtain the almost surely convergence with rate as well as the asymptotic normality of the estimator. As an application, the asymptotic (1 − ζ) confidence interval of the regression operator is also presented (0 < ζ < 1). Finally, the simulation study is carried out to show the finite-sample performances of the estimator.

KEYWORDS:

• Asymptotic properties
• functional stationary ergodic data
• kernel regression estimation
• randomly censorship.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G20
• 62G08
• 62G35

Acknowledgment

The authors would like to thank both the anonymous referees and the Editor in Chief, Prof. N. Balakrishnan for their constructive suggestions that have led to improve the presentation of paper substantially.

Funding

This work is supported by the National Social Science Fund of China [grant number 14ATJ005], the National Natural Science Foundation of China [grant number 11501005].