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Ridge-Type Pretest and Shrinkage Estimation Strategies in Spatial Error Models with an Application to a Real Data Example

Author

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  • Marwan Al-Momani

    (Department of Mathematics, College of Sciences, University of Sharjah, Sharjah P.O. Box 27272, United Arab Emirates)

  • Mohammad Arashi

    (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran
    Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa)

Abstract

Spatial regression models are widely available across several disciplines, such as functional magnetic resonance imaging analysis, econometrics, and house price analysis. In nature, sparsity occurs when a limited number of factors strongly impact overall variation. Sparse covariance structures are common in spatial regression models. The spatial error model is a significant spatial regression model that focuses on the geographical dependence present in the error terms rather than the response variable. This study proposes an effective approach using the pretest and shrinkage ridge estimators for estimating the vector of regression coefficients in the spatial error mode, considering insignificant coefficients and multicollinearity among regressors. The study compares the performance of the proposed estimators with the maximum likelihood estimator and assesses their efficacy using real-world data and bootstrapping techniques for comparison purposes.

Suggested Citation

  • Marwan Al-Momani & Mohammad Arashi, 2024. "Ridge-Type Pretest and Shrinkage Estimation Strategies in Spatial Error Models with an Application to a Real Data Example," Mathematics, MDPI, vol. 12(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:390-:d:1326543
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    References listed on IDEAS

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    2. Gilley, Otis W. & Pace, R. Kelley, 1996. "On the Harrison and Rubinfeld Data," Journal of Environmental Economics and Management, Elsevier, vol. 31(3), pages 403-405, November.
    3. Pace, R Kelley & Gilley, Otis W, 1997. "Using the Spatial Configuration of the Data to Improve Estimation," The Journal of Real Estate Finance and Economics, Springer, vol. 14(3), pages 333-340, May.
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    5. Sévérien Nkurunziza & Marwan Al-Momani & Eric Yu Yin Lin, 2016. "Shrinkage and LASSO strategies in high-dimensional heteroscedastic models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(15), pages 4454-4470, August.
    6. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
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