Prediction Intervals for Summed Totals.

J. A. Dei Rossi

ResearchPublished 1968

Methods for calculating prediction intervals for total estimates that are sums of individually derived estimates. Special attention is given to the problem encountered when the variances of each of the individually derived estimates cannot be assumed to be equal. This problem is essentially identical to the well-known Behren-Fisher problem except that here the context is one of deriving a "t-ratio" for summed means rather than for the difference between means. Thus, for the case of unequal variances, the prediction interval is based on a statistic with an approximate t-distribution and the interval itself must be viewed as an approximation. This should cause no difficulty, however, since such intervals can be viewed as reasonably accurate representations of the true intervals. Examples are given for each of the cases considered.

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Dei Rossi, J. A., Prediction Intervals for Summed Totals. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/research_memoranda/RM5806.html.
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