Abstract
In this paper we study the estimation of the spatial long memory parameter for stationary long range dependent random fields using wavelet methods. We first show the relation between the wavelet coefficients of the random fields and its long memory parameter. Based on this relation, we construct a log-regression wavelet estimator of the long memory parameter. Under some mild regularity assumptions, the asymptotic properties of the estimators are investigated. Finally, a small simulation study illustrates the method.
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Acknowledgments
We sincerely wish to thank two referees for their queries and many insightful remarks and suggestions which have led to improving the presentation of the results. We would also like to thank Zhengyu Xie for helping us with the simulations. This work has been supported by National Natural Science Foundation of China (NSFC) Grant (No.11171147), and has also received funds from Qing Lan Project, Jiangsu Province, and from the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No.708044).
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Wang, L., Wang, J. Wavelet estimation of the memory parameter for long range dependent random fields. Stat Papers 55, 1145–1158 (2014). https://doi.org/10.1007/s00362-013-0558-2
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DOI: https://doi.org/10.1007/s00362-013-0558-2
Keywords
- Asymptotic property
- Long memory parameter
- Long range dependent random fields
- Wavelet coefficients
- Wavelet estimation