“Inference On Distribution Functions Under Measurement Error” by Yoon-Jae Whang
Seoul National University
This paper is concerned with inference on the cumulative distribution function (cdf) Fx* in the classical measurement error model X = X* + ϵ. We show validity of asymptotic and bootstrap approximations for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator of Hall and Lahiri (2008) and Fx*. We allow the density of ϵ to be ordinary or super smooth, or to be estimated by repeated measurements. 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 densities, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.