proposition 11.93 $Z=\sqrt{q}$

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:2902 · p. 405

Rests on

depends_on corollary 11.82 The one degree of freedom tail ¶
- depends_on definition 11.80 Chi-squared ¶
- proves proof ch:09-probability-statistics@proof-35 ¶
depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶
- depends_on definition 11.70 Profile likelihood ¶
  - depends_on definition 11.54 Likelihood ¶
    - depends_on definition 11.53 Statistical model ¶
  - depends_on definition 11.56 Maximum-likelihood estimator ¶
    - depends_on definition 11.54 Likelihood ¶ ↺
- depends_on theorem 11.88 Wilks ¶
  - depends_on definition 11.80 Chi-squared ¶ ↺
  - depends_on definition 11.87 Likelihood-ratio test statistic ¶
    - depends_on definition 11.54 Likelihood ¶ ↺
    - depends_on definition 11.56 Maximum-likelihood estimator ¶ ↺
    - depends_on definition 11.70 Profile likelihood ¶ ↺
  - 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 definition 11.53 Statistical model ¶ ↺
  - depends_on lemma 11.83 Gaussian quadratic forms ¶
    - depends_on definition 11.80 Chi-squared ¶ ↺
    - proves proof ch:09-probability-statistics@proof-36 ¶
  - depends_on lemma 11.52 Slutsky ¶
    - depends_on definition 11.21 Distribution function ¶
      - depends_on definition 11.20 Density ¶
    - proves proof ch:09-probability-statistics@proof-20 ¶
    - proves proof ch:09-probability-statistics@proof-21 ¶
  - depends_on theorem 11.67 Asymptotics of the MLE ¶
    - depends_on corollary 11.51 Weak law of large numbers ¶
      - depends_on lemma 11.50 Markov and Chebyshev inequalities ¶
      - proves proof ch:09-probability-statistics@proof-19 ¶
    - depends_on definition 11.56 Maximum-likelihood estimator ¶ ↺
    - depends_on definition 11.59 Regularity conditions ¶ ↺
    - 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 ¶
    - depends_on lemma 11.52 Slutsky ¶ ↺
    - depends_on theorem 11.46 Central limit theorem, Lindeberg–Lévy ¶
      - depends_on lemma 11.44 Second-order expansion ¶
      - depends_on proposition 11.43 Elementary properties ¶
      - depends_on theorem 11.45 Lévy's continuity theorem ¶
      - proves proof ch:09-probability-statistics@proof-17 ¶
    - proves proof ch:09-probability-statistics@proof-27 ¶
    - proves proof ch:09-probability-statistics@proof-29 ¶
  - proves proof ch:09-probability-statistics@proof-38 ¶
  - proves proof ch:09-probability-statistics@proof-39 ¶
  - proves proof ch:09-probability-statistics@prooflink-4 ¶
- proves proof ch:09-probability-statistics@proof-40 ¶
depends_on definition 11.92 Significance ¶
- depends_on definition 11.75 $p$-value ¶
  - depends_on definition 11.74 Hypotheses and tests ¶
    - depends_on definition 11.53 Statistical model ¶ ↺
depends_on equation 11.86 eq:prob-chernoff ¶
proves proof ch:09-probability-statistics@proof-41 ¶

Supports

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 ¶

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 one degree of freedom tail	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2921
`depends_on`	→	Degrees of freedom with nuisance parameters	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2921
`depends_on`	→	Significance	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2921
`depends_on`	→	eq:prob-chernoff	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2921
`depends_on`	←	Degrading a local five sigma	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3350
`depends_on`	←	Why categorizing helps, and by how much	declared	parts/11-qft-standard-model/15-exp-higgs-discovery.tex:1363
`depends_on`	←	Sensitivity is set by ratio, not by rate	declared	parts/11-qft-standard-model/15-exp-higgs-discovery.tex:1103
`proves`	←	ch:09-probability-statistics@proof-41	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2924