Optimal subsampling for double generalized linear models with heterogeneous massive data

With the development of information technology, massive data under heterogeneous characteristics are generated in the economic, financial, and other fields. Traditional statistical models and existing statistical methods are often inadequate for handling dispersion modeling problems with heterogeneous massive data. In this article, the optimal subsampling of double generalized linear models is studied in heterogeneous massive data environments. Under certain conditions, the optimal subsampling probabilities of the double generalized linear models with heterogeneous data are derived based on the A-optimality criterion and L-optimality criterion, respectively. Furthermore, a two-step algorithm based on uniform sampling is developed, and the asymptotic properties of the subsample estimator from this algorithm are discussed. The results of numerical simulations and a real example show that the algorithm can improve estimation accuracy and decrease computational costs to some extent.