lemma A.211 Root-$n$ localisation

open in the book · appendices/A-long-proofs.tex:10665 · p. 2894

Rests on

depends_on lemma A.208 The three averages ¶
- 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 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 ¶
      - proves proof ch:09-probability-statistics@proof-18 ¶
    - proves proof ch:09-probability-statistics@proof-19 ¶
- proves proof app:A-long-proofs@proof-126 ¶
depends_on lemma A.209 Uniform third-order remainder ¶
- depends_on definition 11.59 Regularity conditions ¶ ↺
- depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
  - depends_on proposition 7.30 Leibniz rule ¶
    - depends_on definition 7.12 Product of functions ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on equation 7.14 eq:ana-derivh ¶
    - depends_on proposition 7.27 Differentiable implies continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-11 ¶
    - depends_on proposition 7.6 Algebra of limits ¶ ↺
    - proves proof ch:05-real-analysis@proof-14 ¶
  - depends_on theorem 7.34 Rolle ¶
    - depends_on lemma 7.33 Fermat: interior extremum ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
      - depends_on proposition 7.18 Two-sided limit from one-sided limits ¶
      - proves proof ch:05-real-analysis@proof-17 ¶
    - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
      - depends_on proposition 7.22 Sequential characterization ¶
      - depends_on theorem 7.7 Bolzano–Weierstrass ¶
      - proves proof ch:05-real-analysis@proof-9 ¶
    - proves proof ch:05-real-analysis@proof-18 ¶
  - proves proof ch:05-real-analysis@proof-22 ¶
- proves proof app:A-long-proofs@proof-127 ¶
proves proof app:A-long-proofs@proof-129 ¶

Supports

depends_on lemma A.213 The three minima ¶
- depends_on theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶

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`	→	The three averages	declared	appendices/A-long-proofs.tex:10680
`depends_on`	→	Uniform third-order remainder	declared	appendices/A-long-proofs.tex:10680
`depends_on`	←	The three minima	declared	appendices/A-long-proofs.tex:10799
`proves`	←	app:A-long-proofs@proof-129	declared	appendices/A-long-proofs.tex:10683