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            "citation": "C. Radhakrishna Rao, Information and accuracy attainable in the estimation of statistical parameters, Bulletin of the Calcutta Mathematical Society 37(3) (1945), 81–91; 1992 Springer reprint pp.235–247",
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          "citation": "C. Radhakrishna Rao, Information and accuracy attainable in the estimation of statistical parameters, Bulletin of the Calcutta Mathematical Society 37(3) (1945), 81–91; 1992 Springer reprint pp.235–247",
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      "statement": "# Rao: information bounds and a geometry of statistical populations\n\nRao related the covariance of unbiased estimators to the Fisher information in regular probability models. He also used the information matrix as a quadratic metric for neighboring statistical populations, connecting estimation precision with parameter-space geometry.\n\nThe score of a probability model has a controlled covariance with an unbiased estimating function, yielding a lower bound on estimation variance. In several parameters the information matrix organizes the corresponding covariance restrictions. Rao then reads the same matrix as the local squared length between nearby populations and considers geodesic distance. Fisher's information is inherited input; Cramér's independent bound development and Blackwell's conditional/sequential estimation retain separate attribution.\n\n## Scientific scope\n\nDifferentiability, justified differentiation under the integral, integrability/finite variances and the relevant nonsingular information matrix are required; a nondegenerate metric requires an identifiable regular parameterization. The bound need not be attained. Biased estimators, nonregular models and singular parameters are outside this stated scope. The paper's overstrong sufficient-statistic minimality statements and general testing claims are not adopted.\n\n## People and systems\n\nCalyampudi Radhakrishna Rao\n\n\n\n## Original sources\n\n- [C. Radhakrishna Rao, Information and accuracy attainable in the estimation of statistical parameters, Bulletin of the Calcutta Mathematical Society 37(3) (1945), 81–91; 1992 Springer reprint pp.235–247](https://gwern.net/doc/statistics/1992-rao.pdf)\n",
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