High Dimensional Penalized Maximum Likelihood Estimation and Variable Selection in Geostatistics
In high dimensional spatial data analysis,we consider the problem of selecting covariates and estimating parameters in spatial linear models with Gaussian process errors.When the problem is of fixed dimension,namely,with fixed number of covariates,considered the penalized maximum likelihood estimation(PMLE)and proposed a one-step sparse estimator,in which consistency and oracle property are obtained.Here we propose a spatial penalized maximum likelihood estimator with high dimensional covariates.The optimization is carried out through a coordinate descent algorithm.The convergence rate for parameters'estimation and sparsistency of model selection are obtained for the diverging dimen-sion case.Furthermore,a primal-dual witness based argument leads to a non-asymptotic result on the estimation and model selection consistency for the p(>>)n high dimensional case.Monte Carlo results show the proposed methods'better performance than other competitors,and a real GWAS for SNP data and many phenotype of spatially distributed cell-line data is analyzed and shown the discovery under geostatistical model.
spatial statisticshigh dimensional data analysispenalized maximum likelihood estimationprimal-dual witnesscoordinate descent algorithm
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