INFERENCE ON DISTRIBUTION FUNCTIONS UNDER MEASUREMENT ERROR

Karun Adusumilli, Taisuke Otsu and Yoon-Jae Whang

Working Paper Series from Institute of Economic Research, Seoul National University

Abstract: This paper is concerned with inference on the cumulative distribution function (cdf) FX ? in the classical measurement error model X = X ? + . We consider the case where the density of the measurement error 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 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 is known. Our approximation results are applicable to various contexts, such as con?dence bands for FX ? and its quantiles, and for performing various cdf-based tests such as goodness-of-?t 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.

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Related works:
Journal Article: Inference on distribution functions under measurement error (2020)
Working Paper: Inference on distribution functions under measurement error (2020)
Working Paper: Inference on distribution functions under measurement error (2017)
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