lemma A.208 The three averages

open in the book · appendices/A-long-proofs.tex:10508 · p. 2892

Rests on

depends_on lemma 11.61 Score identities ¶
- depends_on definition 11.60 Score and Fisher information ¶
  - depends_on definition 11.53 Statistical model ¶
- depends_on definition 11.59 Regularity conditions ¶
  - depends_on definition 11.60 Score and Fisher information ¶ ↺
  - depends_on definition 11.53 Statistical model ¶ ↺
- proves proof ch:09-probability-statistics@proof-23 ¶
depends_on theorem A.206 Cramér–Wold, and continuous mapping ¶
- 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 $\R$ ¶
- depends_on lemma 11.52 Slutsky ¶
  - depends_on definition 11.21 Distribution function ¶ ↺
  - proves proof ch:09-probability-statistics@proof-20 ¶
  - proves proof ch:09-probability-statistics@proof-21 ¶
depends_on theorem A.205 Weak law under integrability alone ¶
- depends_on corollary 11.51 Weak law of large numbers ¶
  - depends_on lemma 11.50 Markov and Chebyshev inequalities ¶
    - depends_on definition 11.6 Moments, variance, standard deviation ¶
      - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶
    - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
    - proves proof ch:09-probability-statistics@proof-18 ¶
  - proves proof ch:09-probability-statistics@proof-19 ¶
proves proof app:A-long-proofs@proof-126 ¶

Supports

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 ¶ ↺

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 identities	declared	appendices/A-long-proofs.tex:10514
`depends_on`	→	Cramér–Wold, and continuous mapping	declared	appendices/A-long-proofs.tex:10514
`depends_on`	→	Weak law under integrability alone	declared	appendices/A-long-proofs.tex:10514
`depends_on`	←	Uniform quadratic approximation on the $n^{-1/2}$ scale	declared	appendices/A-long-proofs.tex:10627
`depends_on`	←	Root-$n$ localisation	declared	appendices/A-long-proofs.tex:10680
`proves`	←	app:A-long-proofs@proof-126	declared	appendices/A-long-proofs.tex:10517