论文标题
对定期垫{é} rn模型的规律性和振幅参数的关节最大似然估计的渐近研究
An asymptotic study of the joint maximum likelihood estimation of the regularity and the amplitude parameters of a periodized Mat{é}rn model
论文作者
论文摘要
这项工作考虑了使用Stein引入的垫子{é} rn协方差函数的高斯过程插值的参数估计。根据模型采样数据时，研究了定期性和振幅参数的关节最大似然估计的收敛速率。还用固定和估计参数分析了平均集成平方误差，表明最大似然估计的产率在渐近上与与地面真实情况相同。最后，还考虑了观察到的函数是连续函数的Sobolev空间的固定确定性元素的情况，这表明关节估计不会选择规则性参数，就好像固定振幅是固定一样。
This work considers parameter estimation for Gaussian process interpolation with a periodized version of the Mat{é}rn covariance function introduced by Stein. Convergence rates are studied for the joint maximum likelihood estimation of the regularity and the amplitude parameters when the data are sampled according to the model. The mean integrated squared error is also analyzed with fixed and estimated parameters, showing that maximum likelihood estimation yields asymptotically the same error as if the ground truth was known. Finally, the case where the observed function is a fixed deterministic element of a Sobolev space of continuous functions is also considered, suggesting that a joint estimation does not select the regularity parameter as if the amplitude were fixed.
