Nonparametric curve estimation in measurement error problems with conditionally heteroscedastic variances

Abstract

The Supplement [17] contains the proof of (9.12) and a study of the small error setting. It also contains a data-driven upper bound to SX, details of practical implementation and additional simulation results. We consider the problem of estimating the density fX of a latent variable X using replicated observations contaminated by additive errors. Unlike the classical setting, these errors depend on X, which makes standard Fourier deconvolution techniques inappropriate, and we suggest instead a basis expansion approach. Using a basis of Legendre polynomials, we show that it is possible to express the unknown coefficients of the expansion in terms of invertible equations of moments of the obse..