Abstract

We consider deconvolution kernel estimation of a density with left and/or right unknown finite endpoints. More precisely, based on a sample containing measurement errors, we estimate an endpoint by the maximiser of a diagnostic function. Such a function can, for example, be based on the derivative of a density estimator or on the difference of two density estimators. These density estimators use kernel deconvolution techniques introduced by Stefanski and Carroll (1990). The methodology can also be used to estimate the location of a point of discontinuity of a density function. We establish asymptotic properties of the proposed estimators.