Smoothness adaptive average derivative estimation

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作   者：

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

作者机构：

Department of Economics;  C.P. 6128;  Canada CIREQ;  London School of Economics. Houghton Street;  Succursale Centre-ville;  London WC2A 2AE;  Canada;  Universite de Montreal;  McGill University;  Montreal;  QC H3A 2T7;  H3C 3J7;  UK;  805 rue Sherbrooke ouest;  Montreal (Quebec); 

关键词：

density weighted average derivative estimator;  non-parametric estimation; 

期刊名称：

The econometrics journal

i s s n：

1368-4221

年卷期：

2010 年 13 卷 1 期

页   码：

40-62

页   码：

摘   要：

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.