A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
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DOI：
10.1080/01621459.2012.746061
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发表时间：
2013-03-01
影响因子：
3.7
通讯作者：
Yang, Ping
中科院分区：
文献类型：
--
作者：
Liang, Faming;Cheng, Yi Hen;Yang, Ping
高斯地统计模型在空间数据建模中得到了广泛的应用。然而，在计算上实现这种方法是具有挑战性的，因为它需要对一个大的协方差矩阵进行反演，特别是当有大量的观测值时。本文提出了一种基于重采样的随机逼近方法来解决这一挑战。在该方法的每次迭代中，从完整的数据集中抽取一个小的子样本，然后在随机逼近的框架下对参数的当前估计进行相应的更新。由于所提出的方法在每次迭代中只使用一小部分数据，因此它避免了反转大的协方差矩阵，因此可扩展到大型数据集。提出的方法还导致了一种通用的参数估计方法，最大平均对数似然估计，其中包括流行的最大（对数）似然估计（MLE）方法作为一种特殊情况，有望在分析大型数据集方面发挥重要作用。在较温和的条件下，该方法得到的估计量在概率上收敛于一组等价高斯概率测度的参数值，并且估计量是渐近正态分布的。据作者所知，本文是第一个关于一般协方差函数在填充渐近条件下的渐近正态性的研究。该方法通过大型模拟和真实数据集进行了验证。本文的补充材料可在网上获得。
The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation. Since the proposed method makes use of only a small proportion of the data at each iteration, it avoids inverting large covariance matrices and thus is scalable to large datasets. The proposed method also leads to a general parameter estimation approach, maximum mean log-likelihood estimation, which includes the popular maximum (log)-likelihood estimation (MLE) approach as a special case and is expected to play an important role in analyzing large datasets. Under mild conditions, it is shown that the estimator resulting from the proposed method converges in probability to a set of parameter values of equivalent Gaussian probability measures, and that the estimator is asymptotically normally distributed. To the best of the authors' knowledge, the present study is the first one on asymptotic normality under infill asymptotics for general covariance functions. The proposed method is illustrated with large datasets, both simulated and real. Supplementary materials for this article are available online.