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Nonparametric Two-Step Sieve M Estimation And Inference

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  • Hahn, Jinyong
  • Liao, Zhipeng
  • Ridder, Geert

Abstract

This article studies two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. The asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.

Suggested Citation

  • Hahn, Jinyong & Liao, Zhipeng & Ridder, Geert, 2018. "Nonparametric Two-Step Sieve M Estimation And Inference," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1281-1324, December.
  • Handle: RePEc:cup:etheor:v:34:y:2018:i:06:p:1281-1324_00
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    Cited by:

    1. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    2. Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.

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