Estimation of a residual distribution with small numbers of repeated measurements

The authors consider the estimation of a residual distribution for different measurement problems with a common measurement error process. The problem is motivated by issues arising in the analysis of gene expression data but should have application in other similar settings. It is implicitly assumed throughout that there are large numbers of measurements but small numbers of repeated measurements. As a consequence, the distribution of the estimated residuals is a biased estimate of the residual distribution. The authors present two methods for the estimation of the residual distribution with some restriction on the form of the distribution. They give an upper bound for the rate of convergence for an estimator based on the characteristic function and compare its performance with that of another estimator with simulations.