A "reference" algorithm or instrument and its various "distortions" are considered, where the distortions carry some valid information about the reference. The objective is to combine data from the reference and the distortions together in some manner in order to extract information from both the reference, as well as the distortions, and produce improved inference about the true reference algorithm. This is illustrated in terms of m precipitation radars and semiparametric estimation of the reference distribution and the distortion parameters.