Question: 8.8 This exercise generalizes Example 8.1 in two ways. First, the stationary covariance function ????(h) is replaced by a limiting intrinsic covariance function. If the
8.8 This exercise generalizes Example 8.1 in two ways. First, the stationary covariance function ????(h) is replaced by a limiting intrinsic covariance function. If the range parameter ???? tends to ∞ and ????(h) is multiplied by ????, then a limiting IRF-0 random field is obtained with an intrinsic covariance function given by the linear scheme ????I(h)=−|h|. Second, the number of sites is increased from n = 2 sites to n ≥ 2 sites, located at t1 < ··· < tn. It was shown in Eq. (7.6) that the kriging variance is given by
????2 K(t) =
⎧
⎪
⎨
⎪
⎩
2(ti+1 − t)(t − ti
), ti ≤ t ≤ ti+1, 2(t1 − t), t < t1, 2(t − tn), t > tn?
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