Title: On the rates of convergence of Parallelized Averaged Stochastic Gradient Algorithms,
Abstract: The growing interest for high dimensional and functional data analysis led in
the last decade to an important research developing a consequent amount of
techniques. Parallelized algorithms, which consist in distributing and treat
the data into different machines, for example, are a good answer to deal with
large samples taking values in high dimensional spaces. We introduce here a
parallelized averaged stochastic gradient algorithm, which enables to treat
efficiently and recursively the data, and so, without taking care if the
distribution of the data into the machines is uniform. The rate of convergence
in quadratic mean as well as the asymptotic normality of the parallelized
estimates are given, for strongly and locally strongly convex objectives.