Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pureâ€¦ (More)

We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptoticâ€¦ (More)

We establish that a non-Gaussian nonparametric regression model is asymptotically equivalent to a regression model with Gaussian noise. The approximation is in the sense of Le Cam's deÂ®ciencyâ€¦ (More)

We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantumâ€¦ (More)

We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussianâ€¦ (More)

We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids,â€¦ (More)

â€“ We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions f from a class H, but the supremumâ€¦ (More)

We consider a nonparametric model E, generated by independent observations Xi, i = 1, ..., n, with densities p(x, Î¸i), i = 1, ..., n, the parameters of which Î¸i = f(i/n) âˆˆ Î˜ are driven by the valuesâ€¦ (More)

A nonparametric statistical model of small diÂ€usion type is compared with its discretization by a stochastic Euler diÂ€erence scheme. It is shown that the discrete and continuous models areâ€¦ (More)