论文标题
高斯过程的协方差参数的最大似然估计的渐近分析：带有证明的介绍
Asymptotic analysis of maximum likelihood estimation of covariance parameters for Gaussian processes: an introduction with proofs
论文作者
论文摘要
本文介绍了高斯过程的协方差参数估计的渐近分析。考虑最大似然估计。这次介绍的目的是吸引广泛的受众访问，并介绍文献中的一些现有结果和证明技术。考虑了增加的域和固定域渐近设置。在增加域渐进剂的情况下，可以表明，一般而言，协方差参数的所有组成部分都可以通过最大似然始终如一地估计，并且渐近态性具有。相反，在固定域渐进剂下，只能始终估算构成微吸毒参数的协方差参数的某些组成部分。在固定域的渐近造物下，考虑了各向同性Matérn协方差函数的特殊情况。结果表明，只有方差和空间尺度参数的组合是微能量的。勾勒出一致性和渐近正态性证明，以获得最大似然估计器。
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and to present some existing results and proof techniques from the literature. The increasing-domain and fixed-domain asymptotic settings are considered. Under increasing-domain asymptotics, it is shown that in general all the components of the covariance parameter can be estimated consistently by maximum likelihood and that asymptotic normality holds. In contrast, under fixed-domain asymptotics, only some components of the covariance parameter, constituting the microergodic parameter, can be estimated consistently. Under fixed-domain asymptotics, the special case of the family of isotropic Matérn covariance functions is considered. It is shown that only a combination of the variance and spatial scale parameter is microergodic. A consistency and asymptotic normality proof is sketched for maximum likelihood estimators.
