2010 Rietz lecture: When does the screening effect hold?
2010 Rietz lecture: When does the screening effect hold?
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2010年里茨讲座：筛选效应何时成立？
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Stein
中科院分区：
文献类型：
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作者：
M. Stein
在用最优线性预测对均方连续平稳空间过程的点观测值进行插补时，人们经常会发现，插值量主要取决于距离预测值最近的观测值。这种现象被称为屏蔽效应。然而，在某些情况下，屏蔽效应不是在合理的渐近意义上成立的，并且对屏蔽效应的理论支持仅限于观测地点的一些相当特殊的设置。本文探讨了观测地点的条件和渐近筛选效应成立的过程模型。一系列的例子表明，很难形成一个普遍的结果，特别是对于在不同方向上具有不同程度的光滑度的过程，这对于时空过程来说是自然发生的。这些例子引出了一个一般猜想，并证明了这个猜想的两个特例。这一过程的关键条件是它的频谱密度在高频下应该缓慢变化。不满足这种缓慢高频变化条件的型号应谨慎使用。
When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the observation locations. This paper explores conditions on the observation locations and the process model under which an asymptotic screening effect holds. A series of examples shows the difficulty in formulating a general result, especially for processes with different degrees of smoothness in different directions, which can naturally occur for spatial-temporal processes. These examples lead to a general conjecture and two special cases of this conjecture are proven. The key condition on the process is that its spectral density should change slowly at high frequencies. Models not satisfying this condition of slow high-frequency change should be used with caution.