The influence function of semiparametric estimators

Arbeitspapier

Often semiparametric estimators are asymptotically equivalent to a sample average. The object being averaged is referred to as the influence function. The influence function is useful in formulating primitive regularity conditions for asymptotic normality, in efficiency comparions, for bias reduction, and for analyzing robustness. We show that the influence function of a semiparametric estimator can be calculated as the limit of the Gateaux derivative of a parameter with respect to a smooth deviation as the deviation approaches a point mass. We also consider high level and primitive regularity conditions for validity of the influence function calculation. The conditions involve Frechet differentiability, nonparametric convergence rates, stochastic equicontinuity, and small bias conditions. We apply these results to examples.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP44/15

Classification and Topics

• Classification: Wirtschaft ; Semiparametric and Nonparametric Methods: General ; Single Equation Models; Single Variables: Truncated and Censored Models; Switching Regression Models; Threshold Regression Models ; Fiscal Policies and Behavior of Economic Agents: Household ; Time Allocation and Labor Supply
• Subject: Influence function ; semiparametric estimation ; bias correction

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Ichimura, Hidehiko ; Newey, Whitney K.
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2015

Further information

• DOI: doi:10.1920/wp.cem.2015.4415
• Handle: http://hdl.handle.net/10419/130060
• Last update: 04.04.2025, 7:52 AM CEST