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Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

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  • Caragea, Petruta C.
  • Smith, Richard L.
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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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 7 (August)
    Pages: 1417-1440

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1417-1440

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    Keywords: Approximate likelihood Massive data sets Computational efficiency Statistical efficiency analysis Spatial statistics Autoregressive processes on a lattice;

    References

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    1. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. repec:cup:cbooks:9780521496032 is not listed on IDEAS
    3. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296.
    4. Tzeng, ShengLi & Huang, Hsin-Cheng & Cressie, Noel, 2005. "A Fast, Optimal Spatial-Prediction Method for Massive Datasets," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1343-1357, December.
    5. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
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    Cited by:
    1. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    2. Bhat, Chandra R. & Sener, Ipek N. & Eluru, Naveen, 2010. "A flexible spatially dependent discrete choice model: Formulation and application to teenagers' weekday recreational activity participation," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 903-921, September.

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