Georgia Institute of Technology College of Sciences

The problem of estimation of smooth functionals of unknown parameters of statistical models will be discussed in the cases of high-dimensional log-concave location models (joint work with Martin Wahl) and infinite dimensional Gaussian models with unknown covariance operator. In both cases, the minimax optimal error rates have been obtained in the classes of H\”older smooth functionals with precise dependence on the sample size, the complexity of the parameter (its dimension in the case of log-concave location models or the effective rank of the covariance in the case of Gaussian models)  and on the degree of smoothness of the functionals. These rates are attained for different types of estimators based on two different methods of bias reduction in functional estimation.