Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series

Zudi Lu; Ping Cheng

doi:10.1016/s0378-3758(97)00045-1

Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series

Zudi Lu
, Ping Cheng

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

22 Citations (Scopus)

Abstract

Under quite mild conditions on the kernel and on the bandwidth, the distribution-free strong consistency is proved for the kernel regression and the modified kernel regression of an α-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is Σ^∞_j=1j^a-1α(j)^1-1/v < ∞ (a > 1, v > 1) or Σ^∞_j=1j^a-1α(j) < ∞ (a > 1), which is simple and weaker than those in the literature. © 1997 Eisevier Science B.V.

Original language	English
Pages (from-to)	67-86
Journal	Journal of Statistical Planning and Inference
Volume	65
Issue number	1
DOIs	https://doi.org/10.1016/s0378-3758(97)00045-1
Publication status	Published - 1 Dec 1997
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Distribution-free strong consistency
Kernel regression
Modified kernel regression
Nonlinear time series models
α-mixing stationary sequence

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10.1016/s0378-3758(97)00045-1

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title = "Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series",

abstract = "Under quite mild conditions on the kernel and on the bandwidth, the distribution-free strong consistency is proved for the kernel regression and the modified kernel regression of an α-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is Σ∞j=1ja-1α(j)1-1/v < ∞ (a > 1, v > 1) or Σ∞j=1ja-1α(j) < ∞ (a > 1), which is simple and weaker than those in the literature. {\textcopyright} 1997 Eisevier Science B.V.",

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T1 - Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series

AU - Lu, Zudi

AU - Cheng, Ping

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 1997/12/1

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N2 - Under quite mild conditions on the kernel and on the bandwidth, the distribution-free strong consistency is proved for the kernel regression and the modified kernel regression of an α-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is Σ∞j=1ja-1α(j)1-1/v < ∞ (a > 1, v > 1) or Σ∞j=1ja-1α(j) < ∞ (a > 1), which is simple and weaker than those in the literature. © 1997 Eisevier Science B.V.

AB - Under quite mild conditions on the kernel and on the bandwidth, the distribution-free strong consistency is proved for the kernel regression and the modified kernel regression of an α-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is Σ∞j=1ja-1α(j)1-1/v < ∞ (a > 1, v > 1) or Σ∞j=1ja-1α(j) < ∞ (a > 1), which is simple and weaker than those in the literature. © 1997 Eisevier Science B.V.

KW - Distribution-free strong consistency

KW - Kernel regression

KW - Modified kernel regression

KW - Nonlinear time series models

KW - α-mixing stationary sequence

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U2 - 10.1016/s0378-3758(97)00045-1

DO - 10.1016/s0378-3758(97)00045-1

M3 - RGC 21 - Publication in refereed journal

SN - 0378-3758

VL - 65

SP - 67

EP - 86

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 1

ER -

Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series

Abstract

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Research Keywords

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