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高斯过程协方差的筛估计量AI 解读

Maximum likelihood estimation for the covariance $R$ of a zero-mean Gaussian process is considered, with no assumptions on the covariance or the "time" parameter set $T$. It is shown that the likelihood function is a.s. unbounded in general, and a sieve estimator $\hat{R}$ is constructed. The distribution of $\hat{R}$, considered as a process on $T \times T$, can be described exactly if a certain technical assumption is satisfied concerning the bivariate series expansion of $R$…

高斯过程均值函数的筛估计量AI 解读

A new sieve estimator for the mean function $m(t)$ of a general Gaussian process of known covariance is presented. The estimator $\hat{m}(t)$ is given explicitly from the data and has a simple distribution. It is shown that $\hat{m}(t)$ is asymptotically unbiased and consistent (weakly and in mean square) at each $t$, and that $\hat{m}$ is strongly consistent for $m$ in an appropriate norm. No assumptions are made about the "time" parameter or the covariance.