Semivariance

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In spatial statistics, semivariance can be described by

<math>\gamma(h)=\sum_{i=1}^{n(h)}\frac{(z(x+h)-z(x))^2}{n(h)}</math>

where z is a data value at a particular location, h is the distance between data values, and n(h) counts the number of pairs of data values we are given, spaced a distance of h apart.

A plot of the semivariance versus distance between data values is known as a semivariogram, or simply as a variogram.

Semivariance is calculated in the same manner as variance, but only those observations that fall below the mean are included in the calculation.

Semivariance is sometimes described as a measure of downside risk in an investments context.

For skewed distributions, the semivariance can provide additional information that variance does not.

See also

• variance
• geostatistics
• kriging

References

1. Shine, J.A., Wakefield, G.I.: A comparison of supervised imagery classification using analyst-chosen and geostatistically-chosen training sets, 1999, http://www.geovista.psu.edu/sites/geocomp99/Gc99/044/gc_044.htmde:Semivarianz