Smoothness Adaptive Average Derivative Estimation

23 Pages Posted: 15 Feb 2010

See all articles by Marcia Schafgans

Marcia Schafgans

London School of Economics & Political Science (LSE)

Victoria Zinde‐Walsh

McGill University - Department of Economics

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Date Written: 2009-09


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.

Suggested Citation

Schafgans, Marcia and Zinde-Walsh, Victoria, Smoothness Adaptive Average Derivative Estimation (2009-09). Econometrics Journal, Vol. 13, Issue 1, pp. 40-62, February 2010, Available at SSRN: or

Marcia Schafgans (Contact Author)

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Victoria Zinde-Walsh

McGill University - Department of Economics ( email )

855 Sherbrooke Street West
Montreal, QC H3A 2T7
514-398-4834 (Phone)
514-398-4938 (Fax)

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