Density estimation with heteroscedastic error
Aurore Delaigle, Alexander Meister
BERNOULLI | INT STATISTICAL INST | Published : 2008
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for homoscedastic errors become inconsistent. In this paper, we introduce a kernel estimator of a density in the case of heteroscedastic contamination. We establish consistency of the estimator and show that it achieves optimal rates of convergence under quite general conditions. We study the limits of application of the procedure in some extreme situations, where we show that, in some cases, our estimator is consistent, even when the scaling parameter of the error is unb..View full abstract
A, Delaigle's research was supported by a Hellman Fellowship and a Maurice Belz Fellowship. A. Meister's research was partly carried out at the Centre for Mathematics and its Applications, Australian National University, Canberra, Australia.