Asymptotic properties of nonparametric M-estimation for mixing functional data

Jia Chen; Li Xin Zhang

doi:10.1016/j.jspi.2008.05.007

Asymptotic properties of nonparametric M-estimation for mixing functional data

Jia Chen, Li Xin Zhang

Economics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator.

Original language	English
Pages (from-to)	533–546
Number of pages	14
Journal	Journal of Statistical Planning and Inference
Volume	139
Issue number	2
Early online date	22 May 2008
DOIs	https://doi.org/10.1016/j.jspi.2008.05.007
Publication status	Published - 1 Feb 2009

Keywords

αα-Mixing
Asymptotic normality
Consistency
Functional data
Nonparametric M-estimation

Access to Document

10.1016/j.jspi.2008.05.007

Cite this

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abstract = "We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator.",

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AB - We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator.

KW - αα-Mixing

KW - Asymptotic normality

KW - Consistency

KW - Functional data

KW - Nonparametric M-estimation

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