Department of Biostatistics, University of Florida, Gainesville, Florida.
Stat Med. 2019 Oct 15;38(23):4555-4565. doi: 10.1002/sim.8315. Epub 2019 Jul 11.
Spatio-temporal modeling is an active research problem with broad applications. In this problem, proper description and estimation of the data covariance structure plays an important role. In the literature, most available methods assume that the data covariance is stationary and follows a specific parametric form. In practice, however, such assumptions are hardly valid or difficult to verify. In this paper, we propose a new and flexible method for estimating the underlying covariance structure. Our proposed method does not require the covariance to be stationary or follow a parametric form. It can accommodate nonparametric space-time-varying mean structure of the observed data. Under some mild regularity conditions, it is shown that our estimated covariance structure converges to the true covariance structure. The proposed method is also justified numerically by a simulation study and an application to a hand, foot, and mouth disease data.
时空建模是一个具有广泛应用的活跃研究问题。在这个问题中，对数据协方差结构的恰当描述和估计起着重要作用。在文献中，大多数可用的方法假设数据协方差是平稳的，并遵循特定的参数形式。然而，在实践中，这种假设很难成立或难以验证。在本文中，我们提出了一种新的、灵活的估计基础协方差结构的方法。我们提出的方法不需要协方差是平稳的或遵循参数形式。它可以适应观测数据的非参数时空时变均值结构。在一些较温和的正则条件下，证明了我们估计的协方差结构收敛于真实的协方差结构。该方法还通过模拟研究和对手足口病数据的应用进行了数值验证。
