On foundation of statistical inference by C R Rao relating to information inequality

This is the birth centenary year of the living legend and giant in the world of statistics, Prof. Calyampudi Radhakrishna (C R) Rao. This article is a partial reflection of Dr. Rao’s contributions to statistical theory and methodology, including unbiased estimation, variance reduction by sufficiency, efficiency of estimation, information geometry, as well as the application of matrix theory in linear statistical inference. His contributions are so massive, it will be impossible to review all of them. This article will comprise mostly his major discovery, which is Cramér–Rao lower bound and related applications and extensions.