关键词: 异质性, 指数族分布, Maximin似然比估计, 惩罚估计

Abstract: To explore the different traits of heterogeneous data from multiple sources, most of the literature proposed quite complicated models to describe the characteristics of subgroups. However, this paper is focusing on a simple model depicting the homogeneity of subgroups of data. In view of the maximin estimation for Gaussian linear model, this paper proposes the maximin likelihood ratio estimator suitable to the generalized linear model and the penalized estimator in a sparse structure. The method builds a simple and conservative model to reduce the complexity from various data sources by maximizing the minimum of likelihood ratio estimators in all these subgroups. It is of practical significance and widely applicable to exponential family distributions with dependent variables subject to normal, two-point and Poisson distributions, and enriches the research results from the predecessors. Simulation shows that the proposed method can not only detect the homogeneity from the subgroups in a more efficient way, but also forecast out of sample with a higher precision in comparison with the classical ways. Moreover, the proposed method is also relevant to large-scale data in the governmental and economic statistics.

Key words: Heterogeneity, Exponential Family Distribution, Maximin Likelihood Ratio Estimator, Penalized Estimator