# On the Robustness of the Bayes and Wiener Estimators under Model Uncertainty

arXiv: https://arxiv.org/abs/1508.01904 · HTML: https://mlsanity.com/paper/1508.01904/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2015.

## Built on by (most cited first, 3 of 3)

- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk](https://mlsanity.com/paper/2604.18546/) (2026)

## Abstract (arXiv)

This paper deals with the robust estimation problem of a signal given noisy observations. We assume that the actual statistics of the signal and observations belong to a ball about the nominal statistics. This ball is formed by placing a bound on the Tau-divergence family between the actual and the nominal statistics. Then, the robust estimator is obtained by minimizing the mean square error according to the least favorable statistics in that ball. Therefore, we obtain a divergence family-based minimax approach to robust estimation. We show in the case that the signal and observations have no dynamics, the Bayes estimator is the optimal solution. Moreover, in the dynamic case, the optimal offline estimator is the noncausal Wiener filter.