  Logistic regression is a well-known statistical model which is commonly used
in the situation where the output is a binary random variable. It has a wide
range of applications including machine learning, public health, social
sciences, ecology and econometry. In order to estimate the unknown parameters
of logistic regression with data streams arriving sequentially and at high
speed, we focus our attention on a recursive stochastic algorithm. More
precisely, we investigate the asymptotic behavior of a new stochastic Newton
algorithm. It enables to easily update the estimates when the data arrive
sequentially and to have research steps in all directions. We establish the
almost sure convergence of our stochastic Newton algorithm as well as its
asymptotic normality. All our theoretical results are illustrated by numerical
experiments.
