期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 98, 期 7, 页码 1417-1440出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2006.08.010
关键词
approximate likelihood; massive data sets; computational efficiency; statistical efficiency analysis; spatial; statistics; autoregressive processes on a lattice
Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations. (c) 2006 Elsevier Inc. All rights reserved.
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