definition 11.56 Maximum-likelihood estimator

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:1616 · p. 390

ground object -- no derivation owed

Rests on

depends_on definition 11.54 Likelihood ¶
- depends_on definition 11.53 Statistical model ¶

Supports

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 A.214 Wilks, $k$ parameters and $r$ constraints ¶
- depends_on theorem 11.88 Wilks ¶
  - 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 example 11.107 Degrading a local five sigma ¶ ↺
      - depends_on proposition 113.15 Why categorizing helps, and by how much ¶
      - depends_on proposition 113.12 Sensitivity is set by ratio, not by rate ¶
    - depends_on remark 11.90 Failure I: a parameter on the boundary ¶
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 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 proposition 11.72 Nuisance parameters cost information ¶
- depends_on theorem 11.88 Wilks ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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partly declared
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Edges

type	direction	node	provenance	where
`depends_on`	→	Likelihood	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1620
`depends_on`	←	Likelihood-ratio test statistic	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2695
`depends_on`	←	Profile likelihood	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2218
`depends_on`	←	Counting experiment	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1661
`depends_on`	←	Invariance	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1630
`depends_on`	←	Asymptotics of the MLE	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1949