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Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias

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  • Yu, Dalei
  • Bai, Peng
  • Ding, Chang

Abstract

Under flexible distributional assumptions, the adjusted quasi-maximum likelihood (adqml) estimator for mixed regressive, spatial autoregressive model is studied in this paper. The proposed estimation method accommodates the extra uncertainty introduced by the unknown regression coefficients. Moreover, the explicit expressions of theoretical/feasible second-order-bias of the adqml estimator are derived and the difference between them is investigated. The feasible second-order-bias corrected adqml estimator is then designed accordingly for small sample setting. Extensive simulation studies are conducted under both normal and non-normal situations, showing that the quasi-maximum likelihood (qml) estimator suffers from large bias when the sample size is relatively small in comparison to the number of regression coefficients and such bias can be effectively eliminated by the proposed adqml estimation method. The use of the method is then demonstrated in the analysis of the Neighborhood Crimes Data.

Suggested Citation

  • Yu, Dalei & Bai, Peng & Ding, Chang, 2015. "Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 116-135.
    • Handle: RePEc:eee:csdana:v:87:y:2015:i:c:p:116-135
    DOI: 10.1016/j.csda.2015.02.003
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    References listed on IDEAS

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    Cited by:

    1. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    2. Federico Martellosio, 2020. "Non-Identifiability in Network Autoregressions," Papers 2011.11084, arXiv.org, revised Jun 2022.
    3. Yu, Dalei & Ding, Chang & He, Na & Wang, Ruiwu & Zhou, Xiaohua & Shi, Lei, 2019. "Robust estimation and confidence interval in meta-regression models," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 93-118.
    4. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.
    5. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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