Sensitivity analysis of SAR estimators: a numerical approximation

Shuangzhe Liu, Wolfgang Polasek, Richard Sellner

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    The estimation of a spatial autoregressive (SAR) model depends on the spatial correlation parameter ρ in a highly nonlinear way, and the least squares (LS) estimators for ρ cannot be computed in a closed form. In this paper, we propose two simple LS estimators and compare them by distance and covariance properties in order to study the local sensitivity behaviour of these estimators. Using matrix derivatives we calculate the Taylor approximation of the LS estimator in the SAR model up to the second order. In a next step, we compare the covariance structure of the two estimators by Kantorovich inequalities and derive efficiency comparisons by upper bounds. Finally, we explore the quality of our new approximations by a Monte Carlo simulation study. The simulation results show significant computation time reductions and a good approximation behaviour of the SAR LS estimator in the neighborhood of ρ=0, when using a non-spatial LS estimator. The results are encouraging and can be used for further developments like quick diagnostic tools to explore the sensitivity of spatial estimators with respect to the size of the spatial correlation
    Original languageEnglish
    Pages (from-to)325-342
    Number of pages18
    JournalJournal of Statistical Computation and Simulation
    Volume82
    Issue number2
    DOIs
    Publication statusPublished - 2012

    Fingerprint

    Least Squares Estimator
    Numerical Approximation
    Sensitivity analysis
    Sensitivity Analysis
    Estimator
    Spatial Model
    Spatial Correlation
    Autoregressive Model
    Derivatives
    Approximation
    Kantorovich Inequality
    Matrix Derivative
    Covariance Structure
    Diagnostics
    Closed-form
    Monte Carlo Simulation
    Least squares estimator
    Simulation Study
    Upper bound
    Calculate

    Cite this

    Liu, Shuangzhe ; Polasek, Wolfgang ; Sellner, Richard. / Sensitivity analysis of SAR estimators: a numerical approximation. In: Journal of Statistical Computation and Simulation. 2012 ; Vol. 82, No. 2. pp. 325-342.
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    author = "Shuangzhe Liu and Wolfgang Polasek and Richard Sellner",
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    Sensitivity analysis of SAR estimators: a numerical approximation. / Liu, Shuangzhe; Polasek, Wolfgang; Sellner, Richard.

    In: Journal of Statistical Computation and Simulation, Vol. 82, No. 2, 2012, p. 325-342.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Sensitivity analysis of SAR estimators: a numerical approximation

    AU - Liu, Shuangzhe

    AU - Polasek, Wolfgang

    AU - Sellner, Richard

    PY - 2012

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    AB - The estimation of a spatial autoregressive (SAR) model depends on the spatial correlation parameter ρ in a highly nonlinear way, and the least squares (LS) estimators for ρ cannot be computed in a closed form. In this paper, we propose two simple LS estimators and compare them by distance and covariance properties in order to study the local sensitivity behaviour of these estimators. Using matrix derivatives we calculate the Taylor approximation of the LS estimator in the SAR model up to the second order. In a next step, we compare the covariance structure of the two estimators by Kantorovich inequalities and derive efficiency comparisons by upper bounds. Finally, we explore the quality of our new approximations by a Monte Carlo simulation study. The simulation results show significant computation time reductions and a good approximation behaviour of the SAR LS estimator in the neighborhood of ρ=0, when using a non-spatial LS estimator. The results are encouraging and can be used for further developments like quick diagnostic tools to explore the sensitivity of spatial estimators with respect to the size of the spatial correlation

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