标题： 非平稳随机函数的一般卷积模型及其估计 显示英文标题

标题： A Generalized Convolution Model and Estimation for Non-stationary Random Functions

摘要： 标准地质统计学模型假设潜在的随机场具有二阶平稳性。在某些情况下，没有理由期望空间依赖结构在整个感兴趣的区域内是平稳的。本文引入了一种新的二阶非平稳随机场模型，该模型是正交随机测度与空间变异随机加权函数卷积的结果。这个新模型是对常见卷积模型的一般化推广，在其中使用的是非随机加权函数。由此产生的非平稳协方差函数类非常通用且灵活，并且对于适当的随机加权函数族选择，可以检索到已知文献中的闭合形式非平稳协方差函数类。在单一实现和局部平稳性的框架下，我们开发了这些显式非平稳协方差函数类的参数推断方法。从局部变差函数的非参数核估计器出发，结合核平滑方法，发展出一种加权局部最小二乘法来估计参数。性能通过两个真实数据集（土壤和降雨数据）进行了评估。结果显示，所提出的方法在多个标准下优于平稳方法。除了空间预测之外，我们还展示了如何在这种非平稳框架下进行条件模拟。 显示英文摘要

摘要： Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In this paper, we introduce a new model for second order non-stationary Random Functions as a convolution of an orthogonal random measure with a spatially varying random weighting function. This new model is a generalization of the common convolution model where a non-random weighting function is used. The resulting class of non-stationary covariance functions is very general, flexible and allows to retrieve classes of closed-form non-stationary covariance functions known from the literature, for a suitable choices of the random weighting functions family. Under the framework of a single realization and local stationarity, we develop parameter inference procedure of these explicit classes of non-stationary covariance functions. From a local variogram non-parametric kernel estimator, a weighted local least-squares approach in combination with kernel smoothing method is developed to estimate the parameters. Performances are assessed on two real datasets: soil and rainfall data. It is shown in particular that the proposed approach outperforms the stationary one, according to several criteria. Beyond the spatial predictions, we also show how conditional simulations can be carried out in this non-stationary framework.