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Prediction Intervals and a Fixed Rank Prediction Algorithm for Spatial Data with Application to Ocean Color.

机译：空间数据的预测间隔和固定秩预测算法及其在海洋颜色中的应用。

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摘要

In this thesis several issues of spatial prediction are studied. The first part of the thesis concerns prediction variance estimation. In practice rarely (if ever) is the spatial covariance known. Often, prediction is performed after estimated spatial covariance parameters are plugged into the spatial prediction equation. The estimated spatial association parameters are also plugged into the prediction variance of the spatial predictor. However, simply plugging spatial covariance parameter estimates into the prediction variance of the spatial predictor does not take into account the uncertainty in the true values of the spatial covariance parameters. As a result, the plug in prediction variance estimate will underestimate the true prediction variance of the estimated spatial predictor, especially for small datasets. We propose a different way to express the prediction variance of the estimated spatial predictor. Based on this expression, we propose a new estimator of the prediction variance of the estimated spatial predictor using parametric bootstrapping. Our new estimator is compared to three other prediction variance estimators. We confirm that the plug-in prediction variance estimator often underestimates the true prediction variance of the estimated spatial predictor. Our new prediction variance estimator sometimes performs best among the four prediction variance estimators compared.;The prediction method known as kriging requires expensive computation to invert the spatial covariance matrix. The dissertation concentrates in its second part on computationally efficient algorithms for spatial prediction using massive datasets. A recent procedure known as Fixed Rank Kriging is reviewed. The method is much faster than kriging and is easily implemented without assuming stationarity. The model requires the estimation of a matrix which must be positive definite. We present a result that shows when a matrix subtraction of a given form will give a positive definite matrix. Motivated by this result and some simulations, we present an iterative Fixed Rank Kriging algorithm that ensures positive definiteness of the matrix required for prediction.;In the last part of the thesis we implement the modified Fixed Rank Kriging procedure to predict missing observations for very large regions of ocean color. We compares the predictions to those made by other well known methods of spatial prediction.
机译：本文研究了空间预测的几个问题。本文的第一部分涉及预测方差估计。实际上，很少（如果有的话）知道空间协方差。通常，在将估计的空间协方差参数插入空间预测方程之后执行预测。估计的空间关联参数也插入到空间预测变量的预测方差中。但是，仅将空间协方差参数估计值插入空间预测变量的预测方差中并不会考虑空间协方差参数的真实值的不确定性。结果，插入预测方差估计将低估估计的空间预测变量的真实预测方差，尤其是对于小型数据集。我们提出了一种不同的方式来表达估计的空间预测变量的预测方差。基于此表达式，我们提出了使用参数自举对估计的空间预测变量的预测方差进行估计的新方法。我们将新的估算器与其他三个预测方差估算器进行了比较。我们确认插件预测方差估计器经常低估估计的空间预测器的真实预测方差。我们的新预测方差估计量有时在所比较的四个预测方差估计量中表现最好。；被称为克里金法的预测方法需要昂贵的计算才能反转空间协方差矩阵。本文的第二部分集中在使用海量数据集进行空间预测的高效计算算法上。回顾了一种称为固定等级克里金法的最新方法。该方法比克里金法快得多，并且无需假设平稳性即可轻松实现。该模型要求估计必须为正定的矩阵。我们给出一个结果，该结果表明给定形式的矩阵减法何时将给出正定矩阵。受此结果和一些模拟的启发，我们提出了一种迭代的固定秩Kriging算法，该算法可确保预测所需矩阵的正定性。在本文的最后部分，我们实现了改进的固定秩Kriging程序来预测非常大的观测值海洋颜色的区域。我们将预测与通过其他众所周知的空间预测方法得出的预测进行比较。

著录项

  • 作者

    Rivera, Roberto.;

  • 作者单位

    University of California, Santa Barbara.;

  • 授予单位 University of California, Santa Barbara.;
  • 学科 Applied Mathematics.;Statistics.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 216 p.
  • 总页数 216
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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