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Title: Asymptotic properties of the ISE in nonparametric regressions with serially correlated errors
Authors: Wu, X
You, J
Zhou, X
Keywords: Central limit theorem
Integrated square error (ISE)
Kernel smoothing
Law of large numbers
Nonparametric estimators
Nonparametric regression function
Serially correlated errors
Issue Date: 2005
Publisher: Taylor & Francis Inc
Source: Communications in statistics - theory and methods, 2005, v. 34, no. 4, p. 943-953 How to cite?
Journal: Communications in Statistics - Theory and Methods 
Abstract: Ioannides (1992) investigated the asymptotic properties of the integrated square error (ISE) of general kernel estimators of the unknown regression function in nonparametric regression with independent random errors. It is well known, however, that the assumption of independent errors is often violated in practical situations, especially in the analyses of economic data. In this article, we relax this assumption by modeling the errors with a moving average process of infinite order, and establish the asymptotic normality and strong consistency of the ISE by extending the martingale central limit theorem. These results can be used to construct test statistics and make asymptotically efficient statistical inference in nonparametric regressions with serially correlated errors.
ISSN: 0361-0926
DOI: 10.1081/STA-200054445
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