Missing at random in nonparametric regression for functional stationary ergodic data in the functional index model

  • Fatima Akkal Djillali Liabes University of Sidi-Bel-Abbès
  • Mustapha Meghnafi
  • Abbes Rabhi
Keywords: Convergence in probability, Ergodic processes, Functional data analysis, Kernel estimator, Nonparametric estimation, Missing at random, Regression operator

Abstract

The main objective of this paper is to estimate non-parametrically the the estimator for the regression function operator when the observations are linked with a single-index. The functional stationary ergodic data with missing at random (MAR) are considered.In particular, we construct the kernel type estimator of the regression operator, some asymptotic properties such as the convergence rate in probability as well as the asymptotic normality of the estimator are established under some mild conditions respectively. As an application, the asymptotic $(1 -\zeta)$ confidence interval of the regression operator is also presented for $0 < \zeta < 1.$

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Published
2018-12-30
How to Cite
Akkal, F., Meghnafi, M., & Rabhi, A. (2018). Missing at random in nonparametric regression for functional stationary ergodic data in the functional index model. MathLAB Journal, 1(3), 384-398. Retrieved from http://purkh.com/index.php/mathlab/article/view/217
Section
Research Articles