Pitman Estimators: An Asymptotic Variance Revisited

Publisher:
SIAM Publishing
Publication Type:
Journal Article
Citation:
Theory of Probability and its Applications, 2013, 57 (3), pp. 521 - 529
Issue Date:
2013-01
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We provide an analytic expression for the variance of ratio of integral functionals of fractional Brownian motion which arises as an asymptotic variance of Pitman estimators for a location parameter of independent identically distributed observations. The expression is obtained in terms of derivatives of a logarithmic moment of the integral functional of limit likelihood ratio process (LLRP). In the particular case when the LLRP is a geometric Brownian motion, we show that the established expression leads to the known representation of the asymptotic variance of Pitman estimator in terms of Riemann zeta-function.
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