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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.

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.

Suggested Citation

  • Caragea, Petruta C. & Smith, Richard L., 2007. "Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1417-1440, August.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1417-1440
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, 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. repec:eee:csdana:v:56:y:2012:i:12:p:4421-4432 is not listed on IDEAS
    3. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    4. Erhardt, Tobias Michael & Czado, Claudia & Schepsmeier, Ulf, 2015. "Spatial composite likelihood inference using local C-vines," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 74-88.
    5. repec:bla:biomet:v:73:y:2017:i:1:p:31-41 is not listed on IDEAS
    6. 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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