IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v98y2007i7p1417-1440.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00133-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, May.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    2. 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.
    3. Lim, Johan & Lee, Kiseop & Yu, Donghyeon & Liu, Haiyan & Sherman, Michael, 2012. "Parameter estimation in the spatial auto-logistic model with working independent subblocks," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4421-4432.
    4. 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.
    5. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    6. Stanislav Anatolyev & Renat Khabibullin & Artem Prokhorov, 2012. "Reconstructing high dimensional dynamic distributions from distributions of lower dimension," Working Papers 12003, Concordia University, Department of Economics.
    7. 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.
    8. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    9. Acosta, Jonathan & Alegría, Alfredo & Osorio, Felipe & Vallejos, Ronny, 2021. "Assessing the effective sample size for large spatial datasets: A block likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    10. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
    11. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yan Chen & Youran Qi & Qing Liu & Peter Chien, 2018. "Sequential sampling enhanced composite likelihood approach to estimation of social intercorrelations in large-scale networks," Quantitative Marketing and Economics (QME), Springer, vol. 16(4), pages 409-440, December.
    2. Simlai, Prodosh, 2014. "Estimation of variance of housing prices using spatial conditional heteroskedasticity (SARCH) model with an application to Boston housing price data," The Quarterly Review of Economics and Finance, Elsevier, vol. 54(1), pages 17-30.
    3. Das, Debojyoti & Bhatia, Vaneet & Kumar, Surya Bhushan & Basu, Sankarshan, 2022. "Do precious metals hedge crude oil volatility jumps?," International Review of Financial Analysis, Elsevier, vol. 83(C).
    4. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    5. Carlo Altavilla & Raffaella Giacomini & Giuseppe Ragusa, 2017. "Anchoring the yield curve using survey expectations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1055-1068, September.
    6. Fernando Rios-Avila & Gustavo Canavire-Bacarreza, 2018. "Standard-error correction in two-stage optimization models: A quasi–maximum likelihood estimation approach," Stata Journal, StataCorp LP, vol. 18(1), pages 206-222, March.
    7. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    8. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    9. Ayouz, Mourad K. & Remaud, Herve, 2003. "The Internationalization Determinants Of The Small Agro-Food Firms: Hypotheses And Statistical Tests," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association, vol. 5(2), pages 1-27.
    10. Broze, Laurence & Gourieroux, Christian, 1998. "Pseudo-maximum likelihood method, adjusted pseudo-maximum likelihood method and covariance estimators," Journal of Econometrics, Elsevier, vol. 85(1), pages 75-98, July.
    11. Sridhar, Shrihari & Naik, Prasad A. & Kelkar, Ajay, 2017. "Metrics unreliability and marketing overspending," International Journal of Research in Marketing, Elsevier, vol. 34(4), pages 761-779.
    12. Yen, Steven T. & Chern, Wen S. & Lee, Hwang-Jaw, 1991. "Effects Of Income Sources On Household Food Expenditures," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271167, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Ruoxuan Xiong & Allison Koenecke & Michael Powell & Zhu Shen & Joshua T. Vogelstein & Susan Athey, 2021. "Federated Causal Inference in Heterogeneous Observational Data," Papers 2107.11732, arXiv.org, revised Apr 2023.
    14. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    15. Koutmos, Dimitrios, 2012. "An intertemporal capital asset pricing model with heterogeneous expectations," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(5), pages 1176-1187.
    16. Gregory, Allan W. & McCurdy, Thomas H., 1986. "The unbiasedness hypothesis in the forward foreign exchange market: A specification analysis with application to France, Italy, Japan, the United Kingdom and West Germany," European Economic Review, Elsevier, vol. 30(2), pages 365-381, April.
    17. Lanot, Gauthier & Walker, Ian, 1998. "The union/non-union wage differential: An application of semi-parametric methods," Journal of Econometrics, Elsevier, vol. 84(2), pages 327-349, June.
    18. Magnus, Jan R., 2007. "The Asymptotic Variance Of The Pseudo Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 23(5), pages 1022-1032, October.
    19. Özlem Onaran & Engelbert Stockhammer, 2006. "The effect of FDI and foreign trade on wages in the Central and Eastern European Countries in the post-transition era: A sectoral analysis," Department of Economics Working Papers wuwp094, Vienna University of Economics and Business, Department of Economics.
    20. Pan, Wei & Louis, Thomas A., 1999. "Two semi-parametric empirical Bayes estimators," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 185-196, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1417-1440. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.