arXiv 28 Jun 2024 · Econometrics
arXiv:2406.19956 · PDF · DOI · OpenAlex · Extracted main text
Rao (1948) introduced the score test statistic as an alternative to the likelihood ratio and Wald test statistics. In spite of the optimality properties of the score statistic shown in Rao and Poti (1946), the Rao score (RS) test remained unnoticed for almost 20 years. Today, the RS test is part of the “Holy Trinity” of hypothesis testing and has found its place in the Statistics and Econometrics textbooks and related software. Reviewing the history of the RS test we note that remarkable test statistics proposed in the literature earlier or around the time of Rao (1948) mostly from intuition, such as Pearson (1900) goodness-fit-test, Moran (1948) I test for spatial dependence and Durbin and Watson (1950) test for serial correlation, can be given RS test statistic interpretation. At the same time, recent developments in the robust hypothesis testing under certain forms of misspecification, make the RS test an active area of research in Statistics and Econometrics. From our brief account of the history the RS test we conclude that its impact in science goes far beyond its calendar starting point with promising future research activities for many years to come.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Rao, C. R (1948) Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation | 1.000 | 17 | 5 | 100% |
| 2 | Rao, C. R. and Poti, S. J (1946) On locally most powerful tests when alternative are one sided | 1.000 | 8 | 3 | 100% |
| 3 | Pearson, K (1900) On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such tha… | 1.000 | 5 | 3 | 100% |
| 4 | Bera, A. K. and Bilias, Y (2001) Rao's score, Neyman's C($$) and Silvey's LM tests: An essay on historical developments and some new results self | 0.737 | 3 | 2 | 100% |
| 5 | Bera, A. K., Bilias, Y., Yoon, M. J., Dogan, O., and Taspnar, S (2020) Adjustments of Rao’s score test for distributional and local parametric misspecifications self | 0.693 | 5 | 1 | 100% |
| 6 | Kent, J. T (1982) Robust properties of likelihood ratio test | 0.644 | 4 | 1 | 100% |
| 7 | Rao, C. R (1950) Sequential tests of null hypotheses | 0.644 | 4 | 1 | 100% |
| 8 | White, H (1982) Maximum likelihood estimation of misspecified models | 0.644 | 4 | 1 | 100% |
| 9 | Breusch, T. S. and Pagan, A. R (1979) A simple test for heteroscedasticity and random coefficient variation | 0.644 | 2 | 2 | 100% |
| 10 | Durbin, J. and Watson, G. S (1950) Testing for serial correlation in least squares regression: I | 0.644 | 2 | 2 | 100% |
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