lemma 11.83 Gaussian quadratic forms
open in the book ·
parts/02-mathematical-methods/09-probability-statistics.tex:2553
· p. 385
Rests on
- depends_on definition 11.80 Chi-squared ¶
- proves proof ch:09-probability-statistics@proof-36 ¶
Supports
- depends_on corollary 11.84 Residuals about a weighted mean; the Birge ratio ¶
-
depends_on
example 33.15
The six values are mutually inconsistent, and by how
much
¶
- depends_on phenomenon 33.16 The least well determined of the constants ¶
- depends_on theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶
-
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 |
→ | Chi-squared | declared | parts/02-mathematical-methods/09-probability-statistics.tex:2560 |
depends_on |
← | Residuals about a weighted mean; the Birge ratio | declared | parts/02-mathematical-methods/09-probability-statistics.tex:2607 |
depends_on |
← | The six values are mutually inconsistent, and by how much | declared | parts/03-classical-mechanics/16-exp-cavendish.tex:1171 |
depends_on |
← | Wilks, $k$ parameters and $r$ constraints | declared | appendices/A-long-proofs.tex:10914 |
depends_on |
← | Wilks | declared | parts/02-mathematical-methods/09-probability-statistics.tex:2720 |
proves |
← | ch:09-probability-statistics@proof-36 | declared | parts/02-mathematical-methods/09-probability-statistics.tex:2563 |