Average derivative estimation under measurement error

Hao Dong (), Taisuke Otsu and Luke Taylor

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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 √ 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.

JEL-codes: J1 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Econometric Theory, 2020. ISSN: 1469-4360

Downloads: (external link)
http://eprints.lse.ac.uk/106489/ Open access version. (application/pdf)

Related works:
Journal Article: AVERAGE DERIVATIVE ESTIMATION UNDER MEASUREMENT ERROR (2021)
Working Paper: Average derivative estimation under measurement error (2019)
Working Paper: Average Derivative Estimation Under Measurement Error (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:106489

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