Rate-optimal estimation of mixed semimartingales

Optimal Nonparametric Estimation for Semimartingales

This paper extends a result of Godambe on parametric estimation for discrete time stochastic processes to nonparametric estimation for the continuous time case. Following Hasminskii and Ibragimov (1980), the nonparametric problem is formulated as a parametric one but with infinite dimensional parameter. Let { P } be a family of probability measures such that (D,F,P) is complete , (Ft,t~O) is a ...

Rate - Optimal Graphon Estimation

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with k clu...

Multi-rate optimal state estimation

Optimal full estimation of qubit mixed states

We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where these states are known to lie on the equatorial plane. For the former case we obtain that the optimal measurement does not depend on the prior probability d...

Functional estimation for Lévy measures of semimartingales with Poissonian jumps

We consider semimartingales with jumps that have finite Lévy measures. This paper is devoted to the estimation of integral-type functionals of the Lévy measures, which are sometimes functions on a compact space, and our main interest is the inference from discrete observations. However we first consider the case where continuous observations are obtained. It would give us an important insight t...