Let H be an infinite-dimentional real separable Hilbert space. Given an unknown mapping M : H (arrow) H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point (theta) (subscript 0) ? H of M. These procedures work in appropriate finite...

Let H be an infinite-dimensional real separable Hilbert space. Given an unknown mapping M:H (r)H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point ?o ( H of M. These procedures work in appropriate finite dimensional sub-spaces of...

Let H be an infinite-dimensional real separable Hilbert space. Given an unknown mapping M:H (r)H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point ?o ( H of M. These procedures work in appropriate finite dimensional sub-spaces of...

To obtain consistency results for nonparametric estimators based on stochastic processes relevant in econometrics, we introduce the notions of Hilbert space-valued <italic>L</italic> mixingales and near-epoch dependent arrays, and we prove weak and strong laws of large numbers by using a new exponential...