Adaptive sequential estimation for ergodic diffusion processes in quadratic metric. Part 2: Asymptotic efficiency

TL;DR

This paper proves the asymptotic efficiency of a sequential estimation procedure for ergodic diffusion processes, establishing that it attains the minimax quadratic risk characterized by Pinsker's constant.

Contribution

It demonstrates that the constructed estimation procedure achieves the asymptotic minimax quadratic risk, confirming its optimality in the quadratic metric.

Findings

Pinsker's constant identified as the asymptotic lower bound

Constructed procedure attains the minimax quadratic risk

Proof of asymptotic efficiency for the estimation method

Abstract

Asymptotic efficiency is proved for the constructed in part 1 procedure, i.e. Pinsker's constant is found in the asymptotic lower bound for the minimax quadratic risk. It is shown that the asymptotic minimax quadratic risk of the constructed procedure coincides with this constant.