Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models |
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Authors: | Petru?a C. Caragea Richard L. Smith |
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Affiliation: | a Department of Statistics, Iowa State University, 314 Snedecor Hall, Ames, IA 50011-1210, USA b Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260, USA |
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Abstract: | 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. |
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Keywords: | 62M30 62M10 62F12 62H11 |
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