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Inference on distribution functions under measurement error
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DOI：10.1016/j.jeconom.2019.09.002.png)
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Abstract
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This paper is concerned with inference on the cumulative distribution function (cdf) F-X* in the classical measurement error model X = X* + epsilon. We consider the case where the density of the measurement error E 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 F-X*. We allow the density of epsilon 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 epsilon is known. Our approximation results are applicable to various contexts, such as confidence bands for F-X* 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. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Measurement error
Deconvolution
Confidence band
Stochastic dominance
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