Better Safe Than Sorry: Risk-Aware Nonlinear Bayesian Estimation
Better Safe Than Sorry: Risk-Aware Nonlinear Bayesian Estimation
复制标题
安全总比后悔好：风险意识非线性贝叶斯估计
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Alejandro Ribeiro
中科院分区：
文献类型：
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作者：
Dionysios S. Kalogerias;Luiz F. O. Chamon;George Pappas;Alejandro Ribeiro
尽管最小均方误差（MMSE）估计的简单和直观的解释，其有效性在某些情况下是值得怀疑的。实际上，最小化平均平方误差不提供任何形式的稳定性，因为估计误差的波动性不受约束。当这种波动性在统计上是显著的时，MMSE估计器的平均性能和实现性能之间的差异可以是显著不同的。为了解决这个问题，我们引入了一个新的风险意识的MMSE制定明确约束所涉及的平方误差的预期预测方差的平均性能和风险之间的交易。我们表明，在温和的矩有界性条件下，相应的风险意识的最优解可以明确评估，并具有适当偏置的非线性MMSE估计的形式。我们通过几个数值例子进一步说明了我们的方法的有效性，这也展示了风险意识对风险中性MMSE估计的优势，特别是在涉及偏斜，重尾分布的模型。
Despite the simplicity and intuitive interpretation of minimum mean squared error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of stability, as the volatility of the estimation error is left unconstrained. When this volatility is statistically significant, the difference between the average and realized performance of the MMSE estimator can be drastically different. To address this issue, we introduce a new risk-aware MMSE formulation which trades between mean performance and risk by explicitly constraining the expected predictive variance of the involved squared error. We show that, under mild moment boundedness conditions, the corresponding risk-aware optimal solution can be evaluated explicitly, and has the form of an appropriately biased nonlinear MMSE estimator. We further illustrate the effectiveness of our approach via several numerical examples, which also showcase the advantages of risk-aware against risk-neutral MMSE estimation, especially in models involving skewed, heavy-tailed distributions.