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Remarks on parameter estimation for the drift of fractional brownian sheet

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Abstract

Let \(\{B_{z}^{\alpha, \beta},z\in[0,T]^{2} \}\) be a d-dimensional fractional Brownian sheet with Hurst parameters \((\alpha, \beta)\in(0,\frac{1}{2})^{2}\). We consider the problem of parameter estimation for the drift of fractional Brownian sheet B α,β and construct superefficient James–Stein estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

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Acknowledgements

This work was jointly supported by the Project Mathematical Tianyuan Foundation of China (11226198), NSFC (11171062), NSFC (11201232), NSFC (81001288), NSRC (10023), Innovation Program of Shanghai Municipal Education Commission (12Z-Z063), Priority Academic Program Development of Jiangsu Higher Education Institutions and Major Program of Key Research Center in Financial Risk Management of Jiangsu Universities Philosophy Social Sciences (No. 2012JDXM009).

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  1. School of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Rd., Pukou, Nanjing, P.R. China

    Junfeng Liu

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  1. Junfeng Liu
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Correspondence to Junfeng Liu.

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Liu, J. Remarks on parameter estimation for the drift of fractional brownian sheet. Acta Math Vietnam. 38, 241–253 (2013). https://doi.org/10.1007/s40306-013-0017-0

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