On deconvolution with repeated measurements

Abstract

In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without it. However, if additional data are available, then it is possible to estimate consistently the unknown error density. Data are seldom available directly on the transformation, but repeated, or replicated, measurements increasingly are becoming available. Such data consist of "intrinsic" values that are measured several times, with errors that are generally independent. Working in this setting we treat the nonparametric deconvolution problems of density e..