Inference on distribution functions under measurement error

Adusumilli, Karun, Kurisu, Daisies, Otsu, Taisuke ORCID: 0000-0002-2307-143X and Whang, Yoon-Jae (2020) Inference on distribution functions under measurement error. Journal of Econometrics, 215 (1). 131 - 164. ISSN 0304-4076

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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.

Item Type:	Article
Official URL:	https://www.journals.elsevier.com/journal-of-econo...
Additional Information:	© 2019 Elsevier B.V.
Divisions:	Economics
Subjects:	H Social Sciences > HB Economic Theory
Date Deposited:	29 Nov 2019 10:33
Last Modified:	29 Nov 2024 19:48
URI:	http://eprints.lse.ac.uk/id/eprint/102692

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