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M-estimation for linear models with spatially-correlated errors

Author

Listed:
  • Cui, Hengjian
  • He, Xuming
  • Ng, Kai W.

Abstract

When a linear model is used to analyze spatially correlated data, but the form of the spatial correlogram is unknown or difficult to specify, it is not straightforward to carry out valid statistical inference on regression parameters. We derive the asymptotic distributions for a class of M-estimators, which includes the least squares and the least absolute deviation, so as to provide the basis for valid large-sample inference even when the spatial correlation structure is not taken into account in estimating the regression coefficients.

Suggested Citation

  • Cui, Hengjian & He, Xuming & Ng, Kai W., 2004. "M-estimation for linear models with spatially-correlated errors," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 383-393, March.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:4:p:383-393
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    Citations

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    Cited by:

    1. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    2. Zhou, Zhou & Wu, Wei Biao, 2011. "On linear models with long memory and heavy-tailed errors," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 349-362, February.
    3. Yu Zhang, 2023. "Asymptotic Normality of M-Estimator in Linear Regression Model with Asymptotically Almost Negatively Associated Errors," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    4. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.
    5. Tang, Niansheng & Wang, Wenjun, 2019. "Robust estimation of generalized estimating equations with finite mixture correlation matrices and missing covariates at random for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 640-655.
    6. Dabo-Niang, Sophie & Thiam, Baba, 2010. "Robust quantile estimation and prediction for spatial processes," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1447-1458, September.
    7. Xin Deng & Xuejun Wang, 2018. "Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1069-1090, December.
    8. Takuma Yoshida, 2019. "Two stage smoothing in additive models with missing covariates," Statistical Papers, Springer, vol. 60(6), pages 1803-1826, December.

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