Details

Autor(en) / Beteiligte

• Negri, Ilia

Titel

Efficiency of a Class of Unbiased Estimators for the Invariant Distribution Function of a Diffusion Process

Ist Teil von

• Communications in statistics. Theory and methods, 2010-01, Vol.39 (1), p.177-185

Ort / Verlag

Philadelphia, PA: Taylor & Francis Group

Erscheinungsjahr

2010

Quelle

Taylor & Francis Journals Auto-Holdings Collection

Beschreibungen/Notizen

• We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly consistent and efficient in different metrics. Here we study the properties of optimality for another kind of estimator recently proposed. We consider a class of unbiased estimators and we show that they are also efficient in the sense that their asymptotic risk, defined as the integrated mean square error, attains the same asymptotic minimax lower bound of the empirical distribution function.