Three Scores and 15 Years (1948 – 2023) of Rao's Score Test: A Complete History and Some New Results

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C. R. Rao's work was always inspired by some practical problems. A problem of estimation of linkage parameters arose while Rao was working in R.A. Fisher's genetics laboratory on mice experiments involving mapping chromosomes. Rao wrote and published two papers based on this work. The first paper dealt with the general problem of testing simple and composite hypotheses concerning a vector parameter using scores, derivatives of the log-likelihood function with respect to the individual parameters. (We will call this the Rao Score (RS) test.) The other paper detailed the steps for analyzing the data involving the segregation of several factors in mating of different genotypes and using the RS test for the meta-analysis of testing the equality of parameters coming from different experimental data sets.
The RS test was well ahead of its time. It went unnoticed for very many years. It is fair to say that econometricians can claim major credit in applying RS test in several useful contexts and coming up with neat and elegant formulae test statistics. More recently, statisticians are catching up with innovative applications of RS test.