  In the research field of big data, one of important issues is how to recover
the sequentially changing sets of true features when the data sets arrive
sequentially. The paper presents a general framework for online updating
variable selection and parameter estimation in generalized linear models with
streaming datasets. This is a type of online updating penalty likelihoods with
differentiable or non-differentiable penalty function. The online updating
coordinate descent algorithm is proposed to solve the online updating
optimization problem. Moreover, a tuning parameter selection is suggested in an
online updating way. The selection and estimation consistencies, and the oracle
property are established, theoretically. Our methods are further examined and
illustrated by various numerical examples from both simulation experiments and
a real data analysis.
