On moments of Pitman estimators: the case of fractional Brownian Motion
Alexander Novikov, Nino Kordzakhia, Timothy Ling
TL;DR
This paper investigates the moments of Pitman estimators linked to fractional Brownian motion, providing analytical, numerical, and simulation results to understand their behavior in non-regular estimation problems.
Contribution
It offers new analytical and numerical insights into the moments of Pitman estimators involving fractional Brownian motion, including Monte Carlo simulation data.
Findings
Analytical expressions for moments of Pitman estimators.
Numerical results on estimator moments.
Monte Carlo simulations of variances.
Abstract
In some non-regular 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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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Statistical Distribution Estimation and Applications · Stochastic processes and financial applications