Question: 3.3 If ????(h) is a conditionally positive semidefinite function with ????(0) = 0, show that ????(s, t) = ????(s) + ????(t) ????(t s)

3.3 If −????(h) is a conditionally positive semidefinite function with ????(0) = 0, show that ????(s, t) = ????(s) + ????(t) − ????(t − s) is positive semidefinite. Further show that ????(s, t) represents the covariance function of an intrinsic random field with semivariogram ????(h).

Hint: Given sites t1, ..., tn and an n × 1 coefficient vector

b, it is necessary to show

∑n i,j=1 bi bj

????(ti

, tj

) ≥ 0.

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