Big ball probability with applications in statistical inference

Vladimir Spokoiny (WIAS Berlin)
Wednesday, October 18, 2017 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We derive the bounds on the Kolmogorov distance between probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimensional-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements. We are also interested in the anticoncentration bound for a squared norm of a non-centered Gaussian element in a Hilbert space. All bounds are sharp and cannot be improved in general. We provide a list of motivation examples and applications in statistical inference for the derived results as well.
(joint with Götze, Naumov and Ulyanov)