【主 题】Large dimensional penalized maximum likelihood estimation and variable selection in geostatistics
【时 间】 2017年04月14日（星期五）15:00－16:00
【地 点】 上海财经大学统计与管理学院大楼1208室
【摘 要】In high dimensional spatial data analysis, we consider the problem of selecting covariates and estimating parameters in spatial linear models with Gaussian process errors. Chu et al. (2011) proposed a penalized maximum likelihood estimation(PMLE) and the corresponding one-step sparse estimator, in which consistency and oracle property are obtained. However, in their model, the number of covariates is fixed and small compared to the sample size, clearly a restriction for many practical datasets where the number of covariates is comparable with the sample size. Here, we propose two penalized methods for the spatial data with diverging number of covariates, based on penalized least square estimation and penalized maximum likelihood estimation, respectively. The optimization is carried out through a coordinate descent algorithm. The convergence rate for parameters' estimation error is investigated, and sparsistency results on model selection are obtained. Monte Carlo results show the proposed methods' better performance than other competitors. The proposed methods are applied on a real air quality index data and some useful insight is obtained.