Low order approximations in deconvolution and regression with errors in variables

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A SPECTRAL METHOD FOR DECONVOLVING A DENSITY (2010, methodology): “The traditional approach (see Carroll and Hall, 1988) uses a kernel to stabilize the integral. This is the so-called deconvolution kernel. Recently, Hall and Meister (2007) propose a di¤erent approach.”
Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem (2007, methodology): “This approach has been described by Carroll, Delaigle, and Hall (2007) in the homoscedastic case, where it has been proved that for appropriate choices of ρ2, the regularized estimator has the same asymptotic properties.”
Density Estimation in the Presence of Heteroscedastic Measurement Error (2008, unknown): “Another example of the flexible parametric approach is Carroll and Hall (2004) who only require knowledge of low order moments of the measurement error distribution.”
Density estimation with heteroscedastic error (2008, background): “Recent contributions to density deconvolution include Zhang and Karunamuni (2000), Carroll and Hall (2004), van Es and Uh (2005), Hall and Qiu (2005) and Hall and Meister (2007).”
An alternative view of the deconvolution problem (2008, methodology): “We start by studying the theoretical properties of the low-order approximation developed by Carroll and Hall (2004) .”