Cram\'er Rao

The Cramér-Rao bound (CRB) establishes a fundamental lower limit on the variance of any unbiased estimator, providing a benchmark for evaluating estimator performance. Current research focuses on extending the CRB's applicability to complex scenarios, such as high-dimensional data and estimation problems on Riemannian manifolds, often employing techniques like smoothed estimators and generative models (e.g., normalizing flows) to approximate the bound when analytical expressions are unavailable. This work is significant because it allows for more accurate performance analysis in diverse fields, including image processing and covariance matrix estimation, ultimately leading to improved algorithm design and more reliable inferences.