Pitman estimators

An asymptotic variance revisited

A. Novikov, N. Kordzakhia

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)521-529
    Number of pages9
    JournalTheory of Probability and its Applications
    Volume57
    Issue number3
    DOIs
    Publication statusPublished - 2013

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