Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets
Type
ArticleAuthors
Sun, Ying
Stein, Michael L.
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionEnvironmental Statistics Group
Statistics Program
Date
2016-03-09Online Publication Date
2016-03-09Print Publication Date
2016-01-02Permanent link to this record
http://hdl.handle.net/10754/552300
Metadata
Show full item recordAbstract
For Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n3) operations and O(n2) memory. Various approximation methods have been developed to address the computational difficulties. In this paper, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean.Citation
Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets 2014:00 Journal of Computational and Graphical StatisticsPublisher
Informa UK LimitedAdditional Links
http://www.tandfonline.com/doi/abs/10.1080/10618600.2014.975230ae974a485f413a2113503eed53cd6c53
10.1080/10618600.2014.975230