Title: Efficient estimation of smooth functionals in Gaussian shift models
Authors: Vladimir Koltchinskii - Georgia Institute of Technology (United States)
Mayya Zhilova - Georgia Institute of Technology (United States) [presenting]
Abstract: A problem of estimation of smooth functionals of a high-dimensional parameter of a Gaussian shift model with known covariance operator is studied. We develop asymptotically efficient estimators for functionals of Hoelder smoothness $s$. We show that their mean squared error rate is minimax optimal, at least in the case of finite-dimensional standard Gaussian shift model. Moreover, we determine a sharp threshold on the smoothness $s$ such that for all $s$ above the threshold, the functional can be estimated efficiently in a ``small noise'' setting. The construction of the efficient estimators is crucially based on a bootstrap chain method of bias reduction.