Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Itô process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility...

Minimax Lower Bounds Adityanand Guntuboyina 2011 This thesis deals with lower bounds for the minimax risk in general decision-theoretic problems. Such bounds are useful for assessing the quality of decision rules. After providing a unified treatment of existing techniques, we prove new lower bounds which involve f -divergences, a general class of dissimilarity measures between probability measu...

This paper studies asymptotically optimal estimation and testing procedures for moment condition models using the theory of large deviations (LD). Minimax risk estimation and testing are discussed in details. The aim of the paper is three-fold. First, it studies a moment condition model by treating it as a statistical experiment in Le Cam’s sense, and investigates its large deviation properties...

Suppose Nature picks a probability measure P on a complete separable metric space X at random from a measurable set P fP g Then without knowing a statistician picks a measure Q on X Finally the statistician su ers a loss D P jjQ the relative entropy between P and Q We show that the minimax and maximin values of this game are always equal and there is always a minimax strategy in the closure of ...