On moments of pitman estimators: The case of fractional Brownian motion

Publication Type:
Journal Article
Citation:
Theory of Probability and its Applications, 2014, 58 (4), pp. 601 - 614
Issue Date:
2014-01-01
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© 2014 Society for Industrial and Applied Mathematics. In some nonregular statistical estimation problems, the limiting likelihood processes are functionals of fractional Brownian motion (fBm) with Hurst’s parameter H, 0 < H ≦ 1. In this paper we present several analytical and numerical results on the moments of Pitman estimators represented in the form of integral functionals of fBm. We also provide Monte Carlo simulation results for variances of Pitman and asymptotic maximum likelihood estimators.
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