EconPapers    
Economics at your fingertips  
 

Extremum estimation and numerical derivatives

Han Hong, Aprajit Mahajan and Denis Nekipelov ()

Journal of Econometrics, 2015, vol. 188, issue 1, 250-263

Abstract: Finite-difference approximations are widely used in empirical work to evaluate derivatives of estimated functions. For instance, many standard optimization routines rely on finite-difference formulas for gradient calculations and estimating standard errors. However, the effect of such approximations on the statistical properties of the resulting estimators has only been studied in a few special cases. This paper investigates the impact of commonly used finite-difference methods on the large sample properties of the resulting estimators. We find that first, one needs to adjust the step size as a function of the sample size. Second, higher-order finite difference formulas reduce the asymptotic bias analogous to higher order kernels. Third, we provide weak sufficient conditions for uniform consistency of the finite-difference approximations for gradients and directional derivatives. Fourth, we analyze numerical gradient-based extremum estimators and find that the asymptotic distribution of the resulting estimators may depend on the sequence of step sizes. We state conditions under which the numerical derivative based extremum estimator is consistent and asymptotically normal. Fifth, we generalize our results to semiparametric estimation problems. Finally, we demonstrate that our results apply to a range of nonstandard estimation procedures.

Keywords: Numerical derivative; Entropy condition; Stochastic equicontinuity (search for similar items in EconPapers)
JEL-codes: C14 C52 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407615001207
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:188:y:2015:i:1:p:250-263

DOI: 10.1016/j.jeconom.2014.05.019

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2025-04-22
Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:250-263