We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity we mean a discontinuity (change– point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide ...

We develop priors for Bayes estimation of quantum states that provide minimax state estimation. The relative entropy from the true density operator to a predictive density operator is adopted as a loss function. The proposed prior maximizes the conditional Holevo mutual information, and it is a quantum version of the latent information prior in classical statistics. For one qubit system, we pro...

Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

We establish lower bounds on minimax risks for distributed statistical estimation under a communication budget. Such lower bounds reveal the minimum amount of communication required by any procedure to achieve the centralized minimax-optimal rates for statistical estimation. We study two classes of protocols: one in which machines send messages independently, and a second allowing for interacti...