Contributions to Statistical Theory and Applications
C. R. Rao is a leading figure in statistical science, influencing theory and applications over six decades.
His contributions appear in standard statistics books, including:
Cramer-Rao inequality
Rao-Blackwellization
Rao’s Score Test
Fisher-Rao and Rao Theorems on estimator efficiency
Rao metric and distance
Multivariate Analysis of Variance (MANOVA)
Canonical Variate Analysis
Generalized inverse (g-inverse) of matrices
Cramer-Rao Bound and Rao-Blackwellization are widely cited in statistical and engineering literature.
Quantum Cramer-Rao Bound is significant in Quantum Physics.
Rao-Blackwellization is applied in:
Adaptive sampling
Particle filtering in high-dimensional spaces
Dynamic Bayesian networks
Signal detection and object recognition
Specialized statistical terms associated with Rao:
Rao’s F and U tests in multivariate analysis
Rao’s Quadratic Entropy and Cross Entropy
Characterization theorems: Rao-Rubin, Lau-Rao, Lau-Rao-Shanbhag, Kagan-Linnik-Rao
Two of his influential papers appear in Breakthroughs in Statistics: 1889-1990.
Contributions to combinatorial mathematics, especially in design of experiments:
Developed Orthogonal Arrays (OA), later used by G. Taguchi for industrial quality control.
Introduced the generalized inverse (g-inverse) of matrices, aiding studies in linear models and singular multivariate distributions.
Authored 14 books and 350 research papers, with translations in multiple European and Asian languages.