Hao Dong, Taisuke Otsu, Luke Taylor

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a particularly important class of error distribution as it includes the Gaussian density. We show that under either type of measurement error, despite using nonparametric deconvolution techniques and an estimated error characteristic function, we are able to achieve a √n-rate of convergence for the average derivative estimator. Interestingly, if the measurement error density is symmetric, the asymptotic variance of the average derivative estimator is the same irrespective of whether the error density is estimated or not. The promising finite sample performance of the estimator is shown through a Monte Carlo simulation.

Original languageEnglish
Pages (from-to)1004-1033
Number of pages30
JournalEconometric Theory
Issue number5
Publication statusPublished - 2021 Oct 13
Externally publishedYes

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


Dive into the research topics of 'AVERAGE DERIVATIVE ESTIMATION under MEASUREMENT ERROR'. Together they form a unique fingerprint.

Cite this