theorem 11.46 Central limit theorem, Lindeberg–Lévy
open in the book ·
parts/02-mathematical-methods/09-probability-statistics.tex:1194
· p. 385
Rests on
-
depends_on
lemma 11.44
Second-order expansion
¶
- depends_on definition 11.42 Characteristic function ¶
- proves proof ch:09-probability-statistics@proof-16 ¶
-
depends_on
proposition 11.43
Elementary properties
¶
- depends_on definition 11.42 Characteristic function ¶ ↺
- proves proof ch:09-probability-statistics@proof-15 ¶
-
depends_on
theorem 11.45
Lévy's continuity theorem
¶
- depends_on definition 11.42 Characteristic function ¶ ↺
- proves proof ch:09-probability-statistics@prooflink-1 ¶
- proves proof ch:09-probability-statistics@proof-17 ¶
Supports
- depends_on phenomenon 115.44 A large-scale dipole above $8\times10^{18}$ electronvolts ¶
-
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
corollary 11.89
Degrees of freedom with nuisance
parameters
¶
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 |
→ | Second-order expansion | declared | parts/02-mathematical-methods/09-probability-statistics.tex:1206 |
depends_on |
→ | Elementary properties | declared | parts/02-mathematical-methods/09-probability-statistics.tex:1206 |
depends_on |
→ | Lévy's continuity theorem | declared | parts/02-mathematical-methods/09-probability-statistics.tex:1206 |
depends_on |
← | A large-scale dipole above $8\times10^{18}$ electronvolts | declared | parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2885 |
depends_on |
← | Asymptotics of the MLE | declared | parts/02-mathematical-methods/09-probability-statistics.tex:1949 |
proves |
← | ch:09-probability-statistics@proof-17 | declared | parts/02-mathematical-methods/09-probability-statistics.tex:1209 |