definition 11.59 Regularity conditions

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:1671 · p. 390

ground object -- no derivation owed

Rests on

depends_on definition 11.60 Score and Fisher information ¶
- depends_on definition 11.53 Statistical model ¶
depends_on definition 11.53 Statistical model ¶ ↺

Supports

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 theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶
- 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 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 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 ¶ ↺

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`	→	Score and Fisher information	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1691
`depends_on`	→	Statistical model	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1691
`depends_on`	←	Uniform third-order remainder	declared	appendices/A-long-proofs.tex:10567
`depends_on`	←	Score identities	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1725
`depends_on`	←	Failure I: a parameter on the boundary	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2858
`depends_on`	←	Cramér–Rao inequality	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1849
`depends_on`	←	Asymptotics of the MLE	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1949
`depends_on`	←	Wilks	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2720