Semivariance

In statistics, semivariance is the half, mean, squared Euclidean distance between the measured values z (x _i ) and  z (x _i + h) at the locations  x _i and  x _i + h for the distance or vector  h :

${\displaystyle \lambda (h)={\frac {1}{2\cdot N(h)}}\cdot \sum _{i=1}^{N(h)}\left[z(x_{i})-z(x_{i}+h)\right]^{2}}$

From a geometric point of view, the expression 1/2 [z (x _i ) - z (x _i + h)] ² is the squared, orthogonal distance of a point in the h-scatter diagram from the diagonal  y = x.

A diagram that plots the semivariance against the distance  h is called a semivariogram .

From the model assumption of intrinsic stationarity it follows that the semivariance is an estimator for the halved variance of the increments Z (x _i + h) - Z (x _i ).

See also

• Geostatistics
• Kriging

reference

1. Shine, JA, Wakefield, GI: 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.htm