### Abstract

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.

Original language | English |
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Pages (from-to) | 521-529 |

Number of pages | 9 |

Journal | Theory of Probability and its Applications |

Volume | 57 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

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## Cite this

Novikov, A., & Kordzakhia, N. (2013). Pitman estimators: An asymptotic variance revisited.

*Theory of Probability and its Applications*,*57*(3), 521-529. https://doi.org/10.1137/S0040585X9798614X