Acta Mathematica Vietnamica
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Remarks on parameter estimation for the drift of fractional brownian sheet
Junfeng Liupp. 241-253
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 $B^{\alpha,\beta}$ and construct superefficient James–Stein estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.