Asymptotic Confidence Spheres in Certain Banach Spaces via Covariance Operators

Gaussian limits of processes with values in type 2 Banach spaces can be used to construct asymptotic confidence regions of spherical shape. This is done by estimating the covariance of the limit distribution. Nuclearity of the covariance operators makes it possible to work in subspaces of growing dimension, which is useful for applications. As an example, a Robbins-Monro algorithm is treated.