lemma 11.52 Slutsky

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:1438 · p. 388

Rests on

depends_on definition 11.21 Distribution function ¶
- depends_on definition 11.20 Density ¶
  - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶
proves proof ch:09-probability-statistics@proof-20 ¶
proves proof ch:09-probability-statistics@proof-21 ¶

Supports

depends_on theorem A.206 Cramér–Wold, and continuous mapping ¶
- 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.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 theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶ ↺
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 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 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`	→	Distribution function	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1443
`depends_on`	←	Cramér–Wold, and continuous mapping	declared	appendices/A-long-proofs.tex:10483
`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
`proves`	←	ch:09-probability-statistics@proof-20	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1446
`proves`	←	ch:09-probability-statistics@proof-21	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1532