Portal de Periódicos da CAPES

Aggregation in Geostatistical Problems

1993; Springer Nature (Netherlands); Linguagem: Inglês

10.1007/978-94-011-1739-5_3

2215-1834

Noel Cressie,

Multi-Criteria Decision Making

A random process Z(·) defined on point support has quite different characteristics to those of aggregations of Z(·). For example, $$Z\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s} } \right)$$ has larger variance than $$Z\left( B \right) \equiv \int_B {Z\left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u} } \right)} d\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u} / \int_B {d\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u} } $$ , where $${\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s} }$$ is a point chosen at random within the block B; B is often referred to as the support of Z(B). Suppose that a resource Z(·) is sampled, yielding data $$Z \equiv {\left( {Z\left( {{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s} }_1}} \right), \ldots ,Z\left( {{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s} }_n}} \right)} \right)^\prime }$$ . However, the resource is extracted in blocks B1,…, BN. Let B denote a generic block and suppose that it is desired to predict g(Z(B)) based on the data $${\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{Z} }$$ . The conditional expectation, $$E\left\{ {g\left( {Z\left( B \right)} \right)\left| {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{Z} } \right.} \right\}$$ , minimizes the mean-squared prediction error, but it is impossible to estimate it without making over-utopian parametric assumptions. Current approaches to the problem require knowledge of "block-to-block", and "block-to-sample", parameters that cannot be estimated from the data. This paper proposes alternatively to make the kriging predictor more variable; the result is an optimal predictor for g(Z(B)) that is unbiased for a Gaussian process and approximately unbiased for a non-Gaussian process and sufficiently smooth g.