definition 11.87 Likelihood-ratio test statistic

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:2680 · p. 403

ground object -- no derivation owed

Rests on

depends_on definition 11.54 Likelihood ¶
- depends_on definition 11.53 Statistical model ¶
depends_on definition 11.56 Maximum-likelihood estimator ¶
- depends_on definition 11.54 Likelihood ¶ ↺
depends_on definition 11.70 Profile likelihood ¶
- depends_on definition 11.54 Likelihood ¶ ↺
- depends_on definition 11.56 Maximum-likelihood estimator ¶ ↺

Supports

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 ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Likelihood	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2695
`depends_on`	→	Maximum-likelihood estimator	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2695
`depends_on`	→	Profile likelihood	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2695
`depends_on`	←	The constraint surface	declared	appendices/A-long-proofs.tex:10442
`depends_on`	←	Wilks	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2720