A special representation of a sufficient randomization kernel

Summary A recent paper byKumar/Pathak [1977] contains two examples showing how—in the presence of a boundedly complete sufficient statistic—a randomization kernel can be obtained which yields a random variable equivalent to the original one.It is the purpose of this note to present a simple general theorem containing these examples as special cases. The essential assumption is that the observation can be expressed by a pair of stochastically independent statistics, one of which is ancillary.