Inference on distribution functions under measurement error

Karun Adusumilli, Daisies Kurisu, Taisuke Otsu and Yoon-Jae Whang

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

Abstract: This paper is concerned with inference on the cumulative distribution function (cdf) FX∗ in the classical measurement error model X = X∗ + ε. We consider the case where the density of the measurement error ε is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX∗. We allow the density of ε to be ordinary or super smooth. We also provide several theoretical results on the bootstrap and asymptotic Gumbel approximations of the sup-norm deviation for the case where the density of ε is known. Our approximation results are applicable to various contexts, such as confidence bands for FX∗ and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of X∗, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.

Keywords: measurement error; deconvolution; confidence band; stochastic dominance (search for similar items in EconPapers)
JEL-codes: J1 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2020-03-01
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Published in Journal of Econometrics, 1, March, 2020, 215(1), pp. 131 - 164. ISSN: 0304-4076

Downloads: (external link)
http://eprints.lse.ac.uk/102692/ Open access version. (application/pdf)

Related works:
Journal Article: Inference on distribution functions under measurement error (2020)
Working Paper: Inference on distribution functions under measurement error (2017)
Working Paper: INFERENCE ON DISTRIBUTION FUNCTIONS UNDER MEASUREMENT ERROR
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:ehl:lserod:102692

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().