  Statistical inference is often simplified by sample-splitting. This
simplification comes at the cost of the introduction of randomness not native
to the data. We propose a simple procedure for sequentially aggregating
statistics constructed with multiple splits of the same sample. The user
specifies a bound and a nominal error rate. If the procedure is implemented
twice on the same data, the nominal error rate approximates the chance that the
results differ by more than the bound. We analyze the accuracy of the nominal
error rate and illustrate the application of the procedure to several widely
applied statistical methods.
