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Variable selection and estimation for high‐dimensional spatial autoregressive models

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  • Liqian Cai
  • Tapabrata Maiti

Abstract

Spatial regression models are important tools for many scientific disciplines including economics, business, and social science. In this article, we investigate postmodel selection estimators that apply least squares estimation to the model selected by penalized estimation in high‐dimensional regression models with spatial autoregressive errors. We show that by separating the model selection and estimation process, the postmodel selection estimator performs at least as well as the simultaneous variable selection and estimation method in terms of the rate of convergence. Moreover, under perfect model selection, the ℓ2 rate of convergence is the oracle rate of s/n, compared with the convergence rate of slogp/n in the general case. Here, n is the sample size and p, s are the model dimension and number of significant covariates, respectively. We further provide the convergence rate of the estimation error in the form of sup norm, and ideally the rate can reach as fast as logs/n.

Suggested Citation

  • Liqian Cai & Tapabrata Maiti, 2020. "Variable selection and estimation for high‐dimensional spatial autoregressive models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 587-607, June.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:2:p:587-607
    DOI: 10.1111/sjos.12452
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
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    8. Liqian Cai & Arnab Bhattacharjee & Roger Calantone & Taps Maiti, 2019. "Variable Selection with Spatially Autoregressive Errors: A Generalized Moments LASSO Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 146-200, September.
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    Cited by:

    1. Hou, Li & Jin, Baisuo & Wu, Yuehua, 2024. "Estimation and variable selection for high-dimensional spatial dynamic panel data models," Journal of Econometrics, Elsevier, vol. 238(2).

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