Bianca Neubert
Quadratic functional estimation from observations with multiplicative measurement error
Given observations from a positive random variable contaminated by a multiplicative measurement error, we consider the task of non-parametric estimation of the quadratic functional of the unknown density in a non-asymptotic framework. We propose a kernel estimator based on the empirical Mellin transform using indirect observations. We derive upper bounds for the risk of the estimator over Mellin-Sobolev spaces naturally characterizing regularity and ill-posedness in this model.
