论文标题
在复杂值圆对象的自回归过程上的收缩先验
Shrinkage priors on complex-valued circular-symmetric autoregressive processes
论文作者
论文摘要
我们研究了在功率光谱密度上的收缩率，用于复杂值圆形对称自回归过程。 We construct shrinkage predictive power spectral densities, which asymptotically dominate (i) the Bayesian predictive power spectral density based on the Jeffreys prior and (ii) the estimative power spectral density with the maximal likelihood estimator, where the Kullback-Leibler divergence from the true power spectral density to a predictive power spectral density is adopted as a risk.此外，我们提出了针对Kähler参数空间的客观先验的一般结构，利用带有负本特征值的Laplace-Beltrami操作员的正连续特征功能。我们在复杂价值的固定自动回归型号$ 1 $上介绍了数值实验。
We investigate shrinkage priors on power spectral densities for complex-valued circular-symmetric autoregressive processes. We construct shrinkage predictive power spectral densities, which asymptotically dominate (i) the Bayesian predictive power spectral density based on the Jeffreys prior and (ii) the estimative power spectral density with the maximal likelihood estimator, where the Kullback-Leibler divergence from the true power spectral density to a predictive power spectral density is adopted as a risk. Furthermore, we propose general constructions of objective priors for Kähler parameter spaces, utilizing a positive continuous eigenfunction of the Laplace-Beltrami operator with a negative eigenvalue. We present numerical experiments on a complex-valued stationary autoregressive model of order $1$.
