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        "title": "A measure of asymptotic efficiency for tests of an hypothesis based on the sum of observations (Stanford Technical Report6)",
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        "description": "This record refers to Stanford Technical Report 6, dated 9 November 1951; the 1952 Annals article is a separate publication version. The sum observations are independent copies; finite-tail inequalities require the appropriate side of the mean, and an optimized moment value 1 can give no useful exponential decay. Exponential-rate equivalence does not give exact finite-sample probabilities or Gaussian far-tail accuracy. The testing theorem concerns two simple hypotheses and threshold tests with fixed finite positive error weight, not arbitrary composite/adaptive/dependent testing. No claim of inventing the exponential Markov method or all modern concentration inequalities.",
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          "citation": "A measure of asymptotic efficiency for tests of an hypothesis based on the sum of observations (Stanford Technical Report6)",
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      "statement": "# Chernoff: exponential tail rates and asymptotic test efficiency\n\nChernoff used the optimized exponential moment of a real random variable to bound tails of sums of independent identically distributed observations and identify their exponential decay rate. He then defined an asymptotic efficiency index for threshold tests between two simple hypotheses: the smallest fixed-positive-weight sum of the two error probabilities has a rate independent of that weight. Ratios of the logarithms of these indices compare asymptotic sample requirements.\n\n## Scientific scope\n\nThis record refers to Stanford Technical Report 6, dated 9 November 1951; the 1952 Annals article is a separate publication version. The sum observations are independent copies; finite-tail inequalities require the appropriate side of the mean, and an optimized moment value 1 can give no useful exponential decay. Exponential-rate equivalence does not give exact finite-sample probabilities or Gaussian far-tail accuracy. The testing theorem concerns two simple hypotheses and threshold tests with fixed finite positive error weight, not arbitrary composite/adaptive/dependent testing. No claim of inventing the exponential Markov method or all modern concentration inequalities.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nHerman Chernoff\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [A measure of asymptotic efficiency for tests of an hypothesis based on the sum of observations (Stanford Technical Report6)](https://stacks.stanford.edu/file/druid:sw496fn0032/sw496fn0032_SOL-ONR-06.pdf)\n",
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      "title": "Chernoff: exponential tail rates and asymptotic test efficiency"
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    "title": "Chernoff: exponential tail rates and asymptotic test efficiency",
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    "what_changed": "Chernoff used the optimized exponential moment of a real random variable to bound tails of sums of independent identically distributed observations and identify their exponential decay rate. He then defined an asymptotic efficiency index for threshold tests between two simple hypotheses: the smallest fixed-positive-weight sum of the two error probabilities has a rate independent of that weight. Ratios of the logarithms of these indices compare asymptotic sample requirements.",
    "scope": "Chernoff used the optimized exponential moment of a real random variable to bound tails of sums of independent identically distributed observations and identify their exponential decay rate. He then defined an asymptotic efficiency index for threshold tests between two simple hypotheses: the smallest fixed-positive-weight sum of the two error probabilities has a rate independent of that weight. Ratios of the logarithms of these indices compare asymptotic sample requirements. This record refers to Stanford Technical Report 6, dated 9 November 1951; the 1952 Annals article is a separate publication version. The sum observations are independent copies; finite-tail inequalities require the appropriate side of the mean, and an optimized moment value 1 can give no useful exponential decay. Exponential-rate equivalence does not give exact finite-sample probabilities or Gaussian far-tail accuracy. The testing theorem concerns two simple hypotheses and threshold tests with fixed finite positive error weight, not arbitrary composite/adaptive/dependent testing. No claim of inventing the exponential Markov method or all modern concentration inequalities.",
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