The consistency of estimator under fixed design regression model with NQD errors

Jianhua Shi; Xiaoping Chen; Yong Zhou

doi:10.1186/1029-242X-2014-92

The consistency of estimator under fixed design regression model with NQD errors

Jianhua Shi^*
, Xiaoping Chen
, Yong Zhou

^*Corresponding author for this work

Minnan Normal University
Shanghai University of Finance and Economics
Fujian Normal University
CAS - Academy of Mathematics and System Sciences

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

1 Scopus citations

Abstract

In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e. Y_nk = g(x_nk) + ε_nk for 1 ≤ k ≤ n, where ε_nk are pairwise NQD random errors, x_nk are fixed design points, and g(·) is an unknown function. The nonparametric weighted estimator g_n (·) of g(·) will be introduced and its consistency is studied. As a special case, the consistency result for weighted kernel estimators of the model is established. This extends the earlier work on independent random and dependent random errors to the NQD case.

Original language	English
Article number	92
Journal	Journal of Inequalities and Applications
Volume	2014
Issue number	1
DOIs	https://doi.org/10.1186/1029-242X-2014-92
State	Published - Feb 2014
Externally published	Yes

Keywords

Nonparametric regression model
Pairwise NQD random sequences
Weighted estimator

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10.1186/1029-242X-2014-92

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abstract = "In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e. Ynk = g(xnk) + εnk for 1 ≤ k ≤ n, where εnk are pairwise NQD random errors, xnk are fixed design points, and g(·) is an unknown function. The nonparametric weighted estimator gn (·) of g(·) will be introduced and its consistency is studied. As a special case, the consistency result for weighted kernel estimators of the model is established. This extends the earlier work on independent random and dependent random errors to the NQD case.",

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AU - Shi, Jianhua

AU - Chen, Xiaoping

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N2 - In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e. Ynk = g(xnk) + εnk for 1 ≤ k ≤ n, where εnk are pairwise NQD random errors, xnk are fixed design points, and g(·) is an unknown function. The nonparametric weighted estimator gn (·) of g(·) will be introduced and its consistency is studied. As a special case, the consistency result for weighted kernel estimators of the model is established. This extends the earlier work on independent random and dependent random errors to the NQD case.

AB - In this article, based on NQD samples, we investigate the fixed design nonparametric regression model, i.e. Ynk = g(xnk) + εnk for 1 ≤ k ≤ n, where εnk are pairwise NQD random errors, xnk are fixed design points, and g(·) is an unknown function. The nonparametric weighted estimator gn (·) of g(·) will be introduced and its consistency is studied. As a special case, the consistency result for weighted kernel estimators of the model is established. This extends the earlier work on independent random and dependent random errors to the NQD case.

KW - Nonparametric regression model

KW - Pairwise NQD random sequences

KW - Weighted estimator

UR - https://www.scopus.com/pages/publications/84899717908

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SN - 1025-5834

VL - 2014

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 92

ER -

The consistency of estimator under fixed design regression model with NQD errors

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Keywords

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