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 K\"ahler 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 $1$.

翻译：我们调查了高功率光谱密度的缩缩前哨,以了解复杂值的循环对称自动递减过程。我们建造了缩缩预测力光谱密度,这些微缩预测力光谱密度无一反应地支配了(一) 贝叶斯预测力光谱密度,以杰弗里斯为根据,(二) 估计力光谱密度,以最大概率估计器为根据,采用Kullback-Lebel-Liblerer从真正的电光谱密度向预测力光谱密度的偏差为风险。此外,我们建议对K\'ahler参数空间的客观前哨进行一般构建,利用Laplace-Beltrami操作器的正连续功能,并使用负电子价值。我们用一个复杂价值的固定性自动递增模型进行数字实验,该模型价值为1美元。