 Inference on distribution functions under measurement errorKarun Adusumilli, Daisuke Kurisu, Taisuke Otsu and Yoon-Jae Whang Journal of Econometrics, 2020, vol. 215, issue 1, 131-164 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) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:215:y:2020:i:1:p:131-164 DOI: 10.1016/j.jeconom.2019.09.002 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 |
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