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Least squares estimator for \(\alpha \)-sub-fractional bridges

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Abstract

Let \(\alpha , T>0\). We investigate the asymptotic properties of a least squares estimator (LSE) for the parameter \(\alpha \) of a sub-fractional bridge defined as \(dX_t=-\alpha \frac{X_t}{T-t}dt+dS_t^H, 0\le t<T, X_0=0\), where \(S^H\) is a sub-fractional Brownian motion of Hurst parameter \(H \in \left( \frac{1}{2},1\right) \). Depending on the value of \(\alpha \), we prove that we may have strong consistency or not as \(t\rightarrow T\). When we have consistency, we obtain the rate of this convergence as well.

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Acknowledgments

The authors would like to express our gratitude to the editor and the referees, whose very kind comments helped improve this paper. The authors are very grateful to Professor F.Q. Gao for the useful discussions. Research supported by the Natural Science Foundation of Hunan Province (2015JJ2055), the Education Department Foundation of Hunan Province (14C0456), the Natural Science Foundation of Hunan University of Science and Technology (E54018) and by the Basic Foundation of Weinan Science and Technology Agency and Shaanxi Ministry of Education(2015JCYJ-9, 16JK1267).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Nenghui Kuang

  2. School of Mathematics and Information Science, Weinan Normal University, Weinan, 714000, China

    Bingquan Liu

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  1. Nenghui Kuang
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  2. Bingquan Liu
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Correspondence to Nenghui Kuang.

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Kuang, N., Liu, B. Least squares estimator for \(\alpha \)-sub-fractional bridges. Stat Papers 59, 893–912 (2018). https://doi.org/10.1007/s00362-016-0795-2

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  • DOI: https://doi.org/10.1007/s00362-016-0795-2

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