实时更新超大数据集的变量选择问题研究

大数据在社会经济发展中的广泛应用，给统计学带来新的发展机遇和挑战。本课题研究在线更新超大数据集的变量选择问题。主要内容包括：首先，对于协变量低维时，分别探讨广义线性模型、非线性模型、可加模型、单指标模型和部分线性模型的在线更新算法下的变量选择方法，探索准则更新的表示方法，研究模型选择相合性和参数估计的渐近性质；其次，协变量高维时，分别探讨线性模型、广义线性模型、非参和半参数模型基于在线更新算法下的变量选择，构造被选变量集的在线更新表示及估计参数的在线更新表示方法，研究模型选择相合性和参数估计的渐近性质。低维和高维下分开研究的原因是，考虑变量选择的准则不同，构造累积更新估计量的思路不同。在线更新数据集的变量选择问题的研究具有非常重要的理论价值和应用价值,但是目前很少有相关的研究成果。本课题的研究期待取得理论和方法上的进步。

The widely use of big data in the development of social economics, brings new opportunities and challenges to statistics. Our project is to study variable selection for online updating large-scale datasets. The main study contents mainly include: Firstly, we consider variable selections under the online updating algorithms for generalized linear model, nonlinear model, additive model, single-index model and partial linear models respectively when the dimension of covariates are low, detect the renewable expression for such criterions, study model selection consistency and asymptotic properties of parameter estimators for these models. Secondly, for the high-dimensional covariates, we study variable selection methods of linear model, generalized linear model, nonparametric and semiparametric models based on the online updating algorithms, construct the renewable expressions of selected variables and estimators, study the model selection consistency and asymptotic properties of estimators.The study under the low dimension and high dimension covariates considered respectively is due to that both the variable selection criterions we will use and the renewable estimators we will construct are different for such two cases. The study of variable selection for the online updating large-scale datasets are very meaningful and important both in theory and for application. Up to now, however, few research results can be found in the existing literature. It can be expected that our project could make progress in both theory and methodology.