On moments of Pitman estimators


Séminaire Probabilités & Statistique

14/01/2016 - 14:00 Mme Nino KORDZAKHIA (MacQuarie University, Sydney) Salle 2 - Tour IRMA

The limit theorems for likelihood ratio processes provide a tool for derivation of asymptotic properties of parameter estimators. In the scheme of independent and identically distributed observations, the problem of estimation of a location parameter was first studied by E. J. G. Pitman. He showed that, the generalised Bayesian estimator with the uniform prior (i.e. Pitman estimator), has the minimum variance in the class of equivariant estimators.

In some cases, the limiting likelihood processes are generated by fractional Brownian motion with Hurst's parameter H, 0 < H ≤ 1 (H = 1 corresponds to LAN property).

For these cases we present some results on the moments of limit distribution of Pitman estimators. The Monte Carlo simulation results will be provided for the limit variance of Pitman estimators.