Aggregation in Geostatistical Problems
Aggregation in Geostatistical Problems
复制标题
地统计问题中的聚合
DOI：
10.1007/978-94-011-1739-5_3
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
N. Cressie
中科院分区：
文献类型：
--
作者：
N. Cressie
定义在点支集上的随机过程Z(·)具有与Z(·)的集合性完全不同的特征。例如,(Z\Left({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s}}\Right)\)的方差大于\(Z\Left(B\Right)\Equiv\Int_B{Z\Left({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u}}\Right)}d\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\Thicksim}$}}{u}/\Int_B{d\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u}}\)，其中\({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s}}\)是在块B内随机选择的点；B通常被称为Z(B)的支撑体。假设对资源Z(·)进行采样，得到数据\(Z\EQUEV{\LEFT({Z\Left({{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s}}_1}}\Right)，\ldots，Z\Left({{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{s}}_n}}\Right)}\Right)^\Prime}\)。然而，在块B1、…中提取资源、BN.设B表示一般块，并且假设期望基于数据\({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{Z}来预测g(Z(B))。条件期望\(E\Left\{g\Left({Z\Left(B\Right)}\Right)\Left|{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{Z}}\Right.}\Right\)使均方预测误差最小，但在不作过度乌托邦参数假设的情况下估计它是不可能的。目前解决这一问题的方法需要“块对块”和“块对样本”的知识，而这些参数是无法从数据中估计的。本文提出了另一种方法，使克立格预报器变得更加可变；其结果是对g(Z(B))是无偏的，对于高斯过程是无偏的，对于非高斯过程是近似无偏的，并且g足够光滑。
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.
DOI：
10.2307/2987329
发表时间：
1970-06
期刊：
--
影响因子：
--
作者：
M. Degroot
通讯作者：
M. Degroot