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Smoothness adaptive average derivative estimation

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  • Marcia M. A. Schafgans
  • Victoria Zinde-Walsh

Abstract

Many important models utilize estimation of average derivatives of the conditional mean function. Asymptotic results in the literature on density weighted average derivative estimators (ADE) focus on convergence at parametric rates; this requires making stringent assumptions on smoothness of the underlying density; here we derive asymptotic properties under relaxed smoothness assumptions. We adapt to the unknown smoothness in the model by consistently estimating the optimal bandwidth rate and using linear combinations of ADE estimators for different kernels and bandwidths. Linear combinations of estimators (i) can have smaller asymptotic mean squared error (AMSE) than an estimator with an optimal bandwidth and (ii) when based on estimated optimal rate bandwidth can adapt to unknown smoothness and achieve rate optimality. Our combined estimator minimizes the trace of estimated MSE of linear combinations. Monte Carlo results for ADE confirm good performance of the combined estimator. Copyright (C) The Author(s). Journal compilation (C) Royal Economic Society 2010.

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 13 (2010)
Issue (Month): 1 (02)
Pages: 40-62

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Handle: RePEc:ect:emjrnl:v:13:y:2010:i:1:p:40-62

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Cited by:
  1. Xiaohong Chen & David T. Jacho-Chavez & Oliver Linton, 2012. "Averaging of moment condition estimators," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP26/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, Elsevier, vol. 170(2), pages 442-457.
  3. Yulia Kotlyarova & Marcia M Schafgans & Victoria Zinde-Walsh, 2011. "Adapting Kernel Estimation to Uncertain Smoothness," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2011/557, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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