Using cumulative sums as a tool during error evaluation
Jan Vink1
1Cornell University

Cumulative sums (CUSUM) of errors are used in different disciplines to find systematic errors among random errors. 

The idea behind cumulative sums is that when you suspect that observations with a certain characteristic have non-random errors, a cumulative error will magnify this non-random error even in the presence of random errors. This idea can easily be transferred to applications in applied demography, such as estimates evaluation and evaluating the accuracy of the 2010 differential privacy demonstration products. Small or large population size can be a characteristic that causes non-random errors you want to know about.

Ranking the observations and plotting the cumulative error against the rank is a great visual to inspect the presence of non-random errors.

This paper will show some examples of the use of cumulative errors and proposes a metric that indicates how likely it is that the expected error is independent of a characteristic.