Abstract
This paper deals with the use of higher order mean square successive differences for estimating dispersion when a strong trend is present in the mean value and the method of first differences does not adequately eliminate the trend. The first four moments of the mean square successive second difference, δ22, are derived in samples from an arbitrary population with constant mean (or with linear trend in the means). Because the efficiency of δ22 relative to δ22 increases with β2, the approximate distribution of δ22 is discussed only for a leptokurtic population, specifically for the symmetrical two-tailed exponential population. For populations with varying mean the first two moments of δ22 are given and the effect of trend of the mean values on these moments is discussed. Short tables of the efficiency of the mean square successive second, third, and fourth differences, all relative to s2 are given.
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