Estimation of distribution functions in measurement error models

Abstract

Many practical problems are related to the pointwise estimation of distribution functions when data contains measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control, public health and survey data.Recently, Dattner, Goldenshluger and Juditsky (2011) showed that an estimator based on a direct inversion formula for distribution functions has nice properties when the tail of the characteristic function of the measurement error distribution decays polynomially. In this paper we derive theoretical properties for this estimator for the case where the error distribution is smoother and study its finite sample behavior for different error distributions. Our method is data-driven in the sense that we use only known information, namely, the error distribution and the data. Application of the estimator to estimating hypertension prevalence based on real data is also examined.

Adaptive quantile estimation in deconvolution with unknown error distribution

“…This is not the case under the gamma error distribution which may suggest that the naive estimator profits from the symmetry of the error distribution. Similar behavior was observed also in distribution deconvolution with nonsymmetric error distributions, see Dattner and Reiser [5].…”

Adaptive estimation of a density function using beta kernels

“…However, this constant is large and leads, in numerical simulations, to oversmoothing estimation. In practice, in order to calibrate this constant, we adopt a similar strategy to that presented in Dattner and Reiser (2010).…”

Adaptive Deconvolution on the Non‐negative Real Line

“…Concerning the estimation of the c.d.f. in the convolution model, some papers can be found as Zhang (), Fan (), Hall & Lahiri (), Dattner et al (), Dattner & Reiser () and Dattner et al (). They all present pointwise estimation procedures because the distribution function is not square‐integrable on .…”