definition 11.53 Statistical model

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Supports

• depends_on definition 11.60 Score and Fisher information ¶
  • depends_on definition 11.59 Regularity conditions ¶
    • depends_on lemma A.209 Uniform third-order remainder ¶
      • depends_on corollary A.210 Uniform quadratic approximation on the $n^{-1/2}$ scale ¶
        • depends_on lemma A.213 The three minima ¶
      • depends_on lemma A.211 Root-$n$ localisation ¶
        • depends_on lemma A.213 The three minima ¶ ↺
    • depends_on lemma 11.61 Score identities ¶
      • depends_on example 11.62 Information in a counting experiment ¶
      • depends_on lemma A.208 The three averages ¶
        • depends_on corollary A.210 Uniform quadratic approximation on the $n^{-1/2}$ scale ¶ ↺
        • depends_on lemma A.211 Root-$n$ localisation ¶ ↺
      • depends_on theorem 11.64 Cramér–Rao inequality ¶
        • depends_on corollary 11.65 When the bound is attained ¶
        • depends_on example 11.62 Information in a counting experiment ¶ ↺
      • depends_on theorem 11.67 Asymptotics of the MLE ¶
        • depends_on proposition 11.72 Nuisance parameters cost information ¶
        • depends_on theorem 11.88 Wilks ¶
    • depends_on remark 11.90 Failure I: a parameter on the boundary ¶
    • depends_on theorem 11.64 Cramér–Rao inequality ¶ ↺
    • depends_on theorem 11.67 Asymptotics of the MLE ¶ ↺
    • depends_on theorem 11.88 Wilks ¶ ↺
  • depends_on lemma 11.61 Score identities ¶ ↺
  • depends_on proposition 113.15 Why categorizing helps, and by how much ¶
  • depends_on proposition 11.72 Nuisance parameters cost information ¶ ↺
  • depends_on theorem 11.64 Cramér–Rao inequality ¶ ↺
• depends_on definition 11.54 Likelihood ¶
  • depends_on definition 11.87 Likelihood-ratio test statistic ¶
    • depends_on definition A.203 The constraint surface ¶
      • depends_on lemma A.212 Second-order flatness ¶
        • depends_on lemma A.213 The three minima ¶ ↺
    • depends_on theorem 11.88 Wilks ¶ ↺
  • depends_on definition 11.56 Maximum-likelihood estimator ¶
    • depends_on definition 11.87 Likelihood-ratio test statistic ¶ ↺
    • depends_on definition 11.70 Profile likelihood ¶
      • assumes experiment The Higgs Boson Discovery ¶
        • cites (method) derived bib 08 The ATLAS Experiment at the CERN Large Hadron Collider ¶
        • cites (method) derived bib 08 The ATLAS Experiment at the CERN Large Hadron Collider ¶ ↺
        • cites (method) derived bib 08 The ATLAS Experiment at the CERN Large Hadron Collider ¶ ↺
        • cites (evidence) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (evidence) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
        • … 128 more
      • depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶
        • depends_on example 11.107 Degrading a local five sigma ¶
        • depends_on proposition 11.93 $Z=\sqrt{q}$ ¶
        • depends_on remark 11.90 Failure I: a parameter on the boundary ¶ ↺
      • depends_on definition 11.87 Likelihood-ratio test statistic ¶ ↺
      • depends_on proposition 11.71 Elementary properties ¶
    • depends_on example 11.58 Counting experiment ¶
      • depends_on example 11.62 Information in a counting experiment ¶ ↺
    • depends_on proposition 11.57 Invariance ¶
      • depends_on example 11.58 Counting experiment ¶ ↺
      • depends_on proposition 11.71 Elementary properties ¶ ↺
    • depends_on theorem 11.67 Asymptotics of the MLE ¶ ↺
  • depends_on definition 11.70 Profile likelihood ¶ ↺
• depends_on definition 11.59 Regularity conditions ¶ ↺
• depends_on definition 11.74 Hypotheses and tests ¶
  • depends_on definition 11.75 $p$-value ¶
    • depends_on definition 11.92 Significance ¶
      • depends_on proposition 113.19 The trials factors of the 2012 result ¶
      • depends_on proposition 11.93 $Z=\sqrt{q}$ ¶ ↺
    • depends_on definition 11.96 Local, global, trials factor ¶
      • depends_on corollary 11.105 Trials factor at high significance ¶
      • depends_on definition 11.100 Upcrossings ¶
        • depends_on definition A.218 The hypotheses ¶
        • depends_on lemma A.221 Counting identity ¶
        • depends_on theorem A.219 Rice's formula ¶
        • depends_on theorem 11.101 Davies' bound ¶
        • depends_on theorem 11.103 Level dependence of the mean upcrossing count ¶
        • depends_on theorem 11.102 Rice's formula ¶
      • depends_on proposition 113.19 The trials factors of the 2012 result ¶ ↺
      • depends_on proposition 11.97 The trials factor is at least one ¶
      • depends_on proposition 11.98 Union bound and the naive estimate ¶
        • depends_on example 11.107 Degrading a local five sigma ¶ ↺
    • depends_on proposition 11.76 Uniformity ¶
  • depends_on proposition 11.76 Uniformity ¶ ↺
  • depends_on theorem 11.78 Neyman–Pearson ¶