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Targeted smoothing parameter selection for estimating average causal effects

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  • Jenny Häggström
  • Xavier Luna

Abstract

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. Asymptotic approximations indicate that the smoothing parameters minimizing this mean squared error converges to zero faster than the optimal smoothing parameter for the estimation of the regression functions. In a simulation study we show that the proposed data-driven methods for selecting the smoothing parameters yield lower empirical mean squared error than other methods available such as, e.g., cross-validation. Copyright The Author(s) 2014

Suggested Citation

  • Jenny Häggström & Xavier Luna, 2014. "Targeted smoothing parameter selection for estimating average causal effects," Computational Statistics, Springer, vol. 29(6), pages 1727-1748, December.
  • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1727-1748
    DOI: 10.1007/s00180-014-0515-0
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    References listed on IDEAS

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    1. Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
    2. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
    3. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    4. Ben B. Hansen, 2008. "The prognostic analogue of the propensity score," Biometrika, Biometrika Trust, vol. 95(2), pages 481-488.
    5. Xavier de Luna & Mathias Lundin, 2014. "Sensitivity analysis of the unconfoundedness assumption with an application to an evaluation of college choice effects on earnings," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1767-1784, August.
    6. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    7. Xavier De Luna & Ingeborg Waernbaum & Thomas S. Richardson, 2011. "Covariate selection for the nonparametric estimation of an average treatment effect," Biometrika, Biometrika Trust, vol. 98(4), pages 861-875.
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    Cited by:

    1. Inés Barbeito & Ricardo Cao & Stefan Sperlich, 2023. "Bandwidth selection for statistical matching and prediction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 418-446, March.
    2. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2017. "Joint sufficient dimension reduction and estimation of conditional and average treatment effects," Biometrika, Biometrika Trust, vol. 104(3), pages 583-596.

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