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Non-Nested Testing of Spatial Correlation

Author

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  • Miguel A. Delgado
  • Peter M Robinson

Abstract

We develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or even when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all dimensions; both isotropic models and non-isotropic models can be considered, and a wide variety of correlation structures. In the second case, models involving spatial weight matrices are covered, such as "spatial autoregressive models". The setting is sufficiently general to potentially cover other parametric structures such as certain factor models, and vector-valued observations, and here our preliminary asymptotic theory for parameter estimates is of some independent value. The test statistic is based on a Gaussian pseudo-likelihood ratio, and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct. A small Monte Carlo study of finite-sample performance is included.

Suggested Citation

  • Miguel A. Delgado & Peter M Robinson, 2013. "Non-Nested Testing of Spatial Correlation," STICERD - Econometrics Paper Series 568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:568
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    File URL: http://sticerd.lse.ac.uk/dps/em/em568.pdf
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    References listed on IDEAS

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    1. Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on Rd," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217, January.
    2. Peter Robinson, 2011. "Asymptotic theory for nonparametric regression with spatial data," CeMMAP working papers CWP11/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Robinson, P. M., 1977. "Estimation of a time series model from unequally spaced data," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 9-24, November.
    4. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    5. Kelejian, Harry H. & Piras, Gianfranco, 2011. "An extension of Kelejian's J-test for non-nested spatial models," Regional Science and Urban Economics, Elsevier, vol. 41(3), pages 281-292, May.
    6. 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.
    7. Dunsmuir, W., 1983. "A central limit theorem for estimation in Gaussian stationary time series observed at unequally spaced times," Stochastic Processes and their Applications, Elsevier, vol. 14(3), pages 279-295, March.
    8. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    9. Peter Burridge, 2012. "Improving the J Test in the SARAR Model by Likelihood-based Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 75-107, March.
    10. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    11. Robinson, P.M., 2010. "Efficient estimation of the semiparametric spatial autoregressive model," Journal of Econometrics, Elsevier, vol. 157(1), pages 6-17, July.
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    More about this item

    Keywords

    on-nested test; spatial correlation; pseudo maximum likelihood estimation;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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