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Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples

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Abstract

In this article, we mainly study the consistency properties of wavelet estimator in nonparametric regression model with extended negatively dependent samples. Under some suitable conditions, the pth mean consistency, complete consistency and complete consistency rates of the wavelet estimator in nonparametric regression model with extended negatively dependent samples are obtained. Our results generalize or improve the corresponding ones and the wavelet estimator method for independent and mixing dependent samples to some extent.

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Acknowledgements

The authors are most grateful to the Editor-in-Chief Prof. Christine H. M\(\ddot{u}\)ller and two anonymous referee for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

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Correspondence to Liwang Ding.

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This research is supported by the National Science Foundation of China (11271189, 11461057), the National Science Foundation of Jiangxi (20161BAB201003), Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_0372), 2017 Youth Teacher Research and Development Fund Project of Guangxi University of Finance and Economics (2017QNA01).

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Ding, L., Chen, P. & Li, Y. Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples. Stat Papers 61, 2331–2349 (2020). https://doi.org/10.1007/s00362-018-1050-9

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  • DOI: https://doi.org/10.1007/s00362-018-1050-9

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