The spectral density of a multidimensional stationary process or a homogeneous random field can be inferred through the REgularized Multidimensional Spectral Estimator (REMSE). The latter is characterized by a convex optimization problem subject to moment constraints, in which we search for a spectral density maximizing the -entropy (a generalized definition of entropy) while matching the covariance lags and the -cepstral coefficients (a generalized version of cepstral coefficients) of the underlying process. The Lagrange multiplier theory shows that it is only possible to guarantee the existence of an approximate solution provided that in the dual problem we add a regularization term. We investigate the effect of regularization on the REMSE: increasing the power of regularization corresponds to increasing the -entropy of the estimated spectrum and, as a consequence, it is expected that the estimated model is more robust in the risk-averse sense.

中文翻译：

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分析正则化对 REMSE 的影响

多维平稳过程或均匀随机场的谱密度可以通过正则化多维谱估计器 (REMSE) 推断。后者的特点是受矩约束的凸优化问题，其中我们搜索最大化 - 熵（熵的广义定义）的谱密度，同时匹配协方差滞后和 - 倒谱系数（倒谱系数的广义版本） ) 的底层流程。拉格朗日乘数理论表明，只有在对偶问题中添加正则化项，才能保证近似解的存在。我们研究了正则化对 REMSE 的影响：增加正则化的能力对应于增加估计谱的熵，因此，预计估计模型在风险规避意义上更加稳健。