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Efficient parametric estimation of the spatial autoregressive model

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  • Nicolas Debarsy

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Vincenzo Verardi

    (Louvain Research Institute in Management and Organizations (LouRIM))

  • Catherine Vermandele

    (LMTD - Laboratoire de méthodologie du traitement des données - ULB - Université libre de Bruxelles)

Abstract

This paper introduces a new one-step parametric estimation method for spatial autoregressive (SAR) models, providing an efficient estimator for any error distribution with a defined quantile function. Based on Le Cam's Local Asymptotic Normality (LAN) theory, it extends the maximum likelihood approach to cases like the Laplace distribution, which lacks a globally defined first derivative.\We further develop this estimator for two highly flexible distributions: Tukey's gand-h and Pewsey and Jones's sinh-arcsinh (SAS), designed to capture skewness and non-normal tail weight. These flexible distributions mitigate the risks of distributional misspecification by approximating a wide range of parametric distributions. Monte Carlo simulations assess finite-sample performance, showing that our estimator outperforms traditional parametric spatial methods when the error distribution deviates from normality and is well-approximated by these flexible alternatives.

Suggested Citation

  • Nicolas Debarsy & Vincenzo Verardi & Catherine Vermandele, 2025. "Efficient parametric estimation of the spatial autoregressive model," Working Papers hal-04986047, HAL.
    • Handle: RePEc:hal:wpaper:hal-04986047
    Note: View the original document on HAL open archive server: https://hal.science/hal-04986047v1
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