Cramer-Rao Lower Bound and Information Geometry

By Frank Nielsen. 2013

42 citations recorded by the source corpus.

This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbreaking paper [43], which had a profound impact on subsequent statistical research. Roughly speaking, Rao obtained a lower bound to the variance of an estimator. The importance of this work can be gauged, for instance, by the fact that it has been reprinted in the volume Breakthroughs in Statistics: Foundations and Basic Theory [32]. There have been two major impacts of this work: First, it answers a fundamental question statisticians have always been interested in, namely, how good can a statistical estimator be? Is there a fundamental limit when estimating statistical parameters? Second, it opens up a novel paradigm by introducing differential geometric modeling ideas to the field of Statistics. In recent years, this contribution has led to the birth of a flourishing field of Information Geometry [6].

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

Posterior Meta-Replay for Continual Learning (2021, background): “As we will see below, the KL divergence is for infinitesimal parameter perturbations approximately equal to the Rao distance (Nielsen, 2013).”