Deconvolution density estimation on Lie groups without auxiliary data

Abstract

In this paper, we study density estimation on a general Lie group when data contain measurement errors and the distribution of measurement error is unknown. We estimate the target density without additional observations, such as an observable random sample from the measurement error distribution or repeated measurements. To achieve this, we take a semiparametric approach assuming that the measurement error distribution belongs to a parametric family. We also discuss maximum likelihood estimation for the case where the target density is also parametric. We establish the identifiability of a measurement error model and derive various asymptotic properties for our estimators. The performance of our estimators is demonstrated via simulation studies.