On the Regression Estimation in a Hilbert Space

The problem of estimation of a regression curve in an infinite dimensional space is considered. Such problems arise in the statistics of random processes. Observation data in such processes is a pair whose one component is an element of an infinite dimensional space. It is shown that the finite dimensional projections of observations and the regression curve estimators constructed on their basis give an approximation of a regression function in the initial space. The method of infinite dimensional analysis and in particular the notion of the logarithmic gradient of a distribution function are used.