A New Look at the Statistical Model Identification
1974 · paper · Mathematics and statistics
Introduces the Akaike information criterion for choosing among competing statistical models, defined as minus twice the log maximum likelihood plus twice the number of adjusted parameters. Argues it avoids ambiguities of hypothesis testing and demonstrates it on time series examples.
Checked: PDF from automatica.dei.unipd.it, fetched 5 Oct 2026. Page numbers are those of that PDF.
1 finding
Reference or label The Acknowledgment thanks Prof. Sato "for providing the brain wave data treated in Section V." The brain wave record is analysed in Section VI (Numerical Examples), not Section V (Definition of an Information Criterion).
- p. 7 Acknowledgment
for providing the brain wave data treated in Section V.
- p. 5 Section VI, brain wave example
Fig. 2 shows the results of application of the same type of procedure to a record of brain wave
- p. 7 Acknowledgment
for providing the brain wave data treated in
- p. 7 Acknowledgment
providing the brain wave data treated in Section V.
Judge's note: Page image p.7 (722), Acknowledgment: "brain wave data treated in Section V." Page image p.4 shows Section V, "Definition of an Information Criterion", which contains no data. Section VI, "Numerical Examples", starts on p.4. On p.5 it includes "Fig. 2 shows the results ... to a record of brain wave with N = 1420." The pointer should read Section VI. One reviewer gave N = 1120, but the page prints 1420; this does not affect the finding.
Second check: another model agreed
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10 minor (typos and the like; most checked by the judge only)
Typo MAICE is expanded as "minimum information theoretical criterion (AIC) estimate" in the Abstract but as "minimum information theoretic criterion (AIC) estimate" in the Introduction.
- p. 1 Abstract
minimum information theoretical criterion (AIC) estimate
- p. 1 Introduction
information theoretic criterion (AIC) estimate
- p. 1 Introduction
minimum information theoretic criterion (AIC) estimate
Judge's note: Crops C001-a and C001-b/c show both forms in print. The meaning is the same, so this is a cosmetic consistency point.
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Typo Ungrammatical phrase "will be by far the greater than the rounding errors"; it should read "by far greater than".
- p. 1 Introduction, first paragraph
by far the greater than the rounding errors
Judge's note: Crop C002-a shows the phrase in print. It is a grammatical slip only.
Second check: none (judge only)
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Typo The text has "As was noticed by Lehman [2, p. viii]", while reference [2] reads "E. L. Lehmann, Testing Statistical Hypothesis".
- p. 7 Reference [2]
Testing Statistical Hypothesis
- p. 1 Introduction
As was noticed by Lehman [2, p. viii]
- p. 1 Introduction
As was noticed by Lehman
- p. 7 Reference [2]
E. L. Lehmann, Testing Statistical Hypotheses
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the book title is "Testing Statistical Hypotheses" (plural). The name inconsistency (Lehman in the text versus Lehmann in the reference) is visible in crop C012-c and on the page 7 image. The singular title is in print.
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Typo The biography note prints "Hiortugu Akaike", while the byline gives "HIROTUGU AKAIKE".
- p. 8 Author biography note after references
Hiortugu Akaike
- p. 1 Byline
HIROTUGU
Judge's note: Crops C013-a and C013-b show both spellings in print.
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Typo "periodgram" ("the analysis of the periodgram", "tests based on the periodgrams") is printed where the standard spelling is "periodogram".
- p. 2 Section II
periodgram provides a
- p. 2 Section II
based on the periodgrams is
- p. 2 Sec. II, para. on test of whiteness
the analysis of the periodgram provides a
- p. 2 Sec. II, next paragraph
tests based on the periodgrams
Judge's note: Crops C003-a and C003-b show the spelling in print on page 2. Contrary to one reviewer, reference [38] on page 8 also prints "periodgram" (crop C013-a), so the reference list does not show a correct form. The spelling is still nonstandard.
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Typo The text cites "Gersch and Sharp [25]" (page 3 and twice on page 5), while reference [25] gives "W. Gersch and D. R. Sharpe".
- p. 3 Section III
Gersch and Sharp [25] discussed
- p. 7 Reference [25]
W. Gersch and D. R. Sharpe
Only the authors can say what is right here.
Judge's note: Crop C004-a shows "Sharp" in the text. The page 7 image shows "Sharpe" in reference [25]. The spelling is internally inconsistent; only the authors can confirm the correct form.
Second check: none (judge only)
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Typo "the MAICE among the AR model up to the 50th order" should read "AR models".
- p. 4 Sec. VI, Beveridge's wheat price series
the MAICE among the AR model up
Judge's note: The page 4 image shows the singular form. Page 5 uses "among the AR models up to the 20th order".
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Typo "the choice of eight-order models" should read "eighth-order"; page 4 uses "eighth-order model".
- p. 5 Section VI, first paragraph
the choice of eight-order models
- p. 4 Sec. VI, sunspot example
the MAICE was the eighth-order model
Judge's note: The page 5 top-left text shows "eight-order"; page 4 shows "eighth-order".
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Typo "f(x|θ) is sufficiently closed to g(x)" should read "sufficiently close to".
- p. 5 Section VII, first paragraph
is sufficiently closed to
- p. 5 Section VII, first paragraph
is sufficiently closed to g(x)
- p. 5 Sec. VII, first paragraph
is sufficiently closed to g(r)
Judge's note: Crops C008-a and C008-c show "closed" in print in Section VII.
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Typo Missing comma in the list of results: "AIC(5,3) = 67.48 AIC(6,3) = 67.65".
- p. 5 Sec. VI, list of AIC(p,q) results
AIC(5,3) = 67.48 AIC(6,3) = 67.65
Judge's note: The page 5 image shows no separator after 67.48, while the other items in the list are separated by commas.
Second check: none (judge only)