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Nonequivalence of two least-absolute-deviation estimators for mediation effects

Author

Listed:
  • WenWu Wang

    (Qufu Normal University
    University of Hong Kong)

  • Ping Yu

    (University of Hong Kong)

Abstract

This paper provides two groups of conditions of model consistency in least-absolute-deviation mediation models. Under model consistency, we establish the asymptotic theory of the difference estimator and the product estimator, and show that the two estimators are not only numerically nonequivalent but asymptotically nonequivalent, which is dramatically different from the situation in the least squares mediation analysis where these two estimators are numerically equivalent. In all three possible scenarios of model parameters, both the asymptotic theories and simulation studies show that the product estimator is more efficient than the difference estimator.

Suggested Citation

  • WenWu Wang & Ping Yu, 2023. "Nonequivalence of two least-absolute-deviation estimators for mediation effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 370-387, March.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:1:d:10.1007_s11749-022-00837-8
    DOI: 10.1007/s11749-022-00837-8
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    References listed on IDEAS

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    1. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    2. Tyler J. Vanderweele & Guanglei Hong & Stephanie M. Jones & Joshua L. Brown, 2013. "Mediation and Spillover Effects in Group-Randomized Trials: A Case Study of the 4Rs Educational Intervention," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 469-482, June.
    3. Zhao, Zhibiao & Xiao, Zhijie, 2014. "Efficient Regressions Via Optimally Combining Quantile Information," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1272-1314, December.
    4. Martin A. Lindquist, 2012. "Functional Causal Mediation Analysis With an Application to Brain Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1297-1309, December.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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