theorem 11.64 Cramér–Rao inequality

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:1833 · p. 392

Rests on

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 ¶ ↺
depends_on lemma 11.63 Cauchy–Schwarz for random variables ¶
- depends_on definition 11.11 Covariance and correlation ¶
  - depends_on definition 11.6 Moments, variance, standard deviation ¶
    - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶
      - depends_on definition 11.4 Expectation ¶
      - depends_on proposition 11.2 Elementary rules ¶
      - proves proof ch:09-probability-statistics@proof-2 ¶
  - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
- depends_on definition 11.6 Moments, variance, standard deviation ¶ ↺
- proves proof ch:09-probability-statistics@proof-24 ¶
depends_on lemma 11.61 Score identities ¶
- depends_on definition 11.60 Score and Fisher information ¶ ↺
- depends_on definition 11.59 Regularity conditions ¶ ↺
- proves proof ch:09-probability-statistics@proof-23 ¶
proves proof ch:09-probability-statistics@proof-25 ¶

Supports

depends_on corollary 11.65 When the bound is attained ¶
depends_on example 11.62 Information in a counting experiment ¶

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:1849
`depends_on`	→	Regularity conditions	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1849
`depends_on`	→	Cauchy–Schwarz for random variables	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1849
`depends_on`	→	Score identities	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1849
`depends_on`	←	When the bound is attained	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1892
`depends_on`	←	Information in a counting experiment	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1782
`proves`	←	ch:09-probability-statistics@proof-25	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1861