Nonparametric M-regression for functional ergodic data

作者：Gheriballah Abdelkader; Laksaci Ali^*; Sekkal Soumeya

来源：Statistics & Probability Letters, 2013, 83(3): 902-908.

DOI：10.1016/j.spl.2012.12.004

• Functional data
• Kernel estimate
• Nonparametric model
• Robust estimation
• Ergodic data

Let (X-i, Y-l)(i=1,...,n) be a sequence of stationary ergodic processes valued in F x R, where is a semi-metric space. We consider the problem of estimating the regression function of Y-i given X-i by the robust M-estimation method. The principal aim of this work is to prove the almost complete convergence (with rate) for the proposed estimator. This result is obtained under a stationary ergodic process assumption, without using traditional mixing conditions.

• 出版日期2013-3