example 11.107 Degrading a local five sigma

Rests on

• 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 proposition 11.93 $Z=\sqrt{q}$ ¶
  • 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 11.92 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 ¶
• depends_on proposition 11.98 Union bound and the naive estimate ¶
  • depends_on definition 11.96 Local, global, trials factor ¶
    • depends_on definition 11.75 $p$-value ¶ ↺
    • depends_on equation 11.89 eq:prob-p-one-sided ¶
    • depends_on equation 11.88 eq:prob-q0 ¶
  • proves proof ch:09-probability-statistics@proof-43 ¶
• depends_on theorem 11.101 Davies' bound ¶
  • depends_on definition 11.100 Upcrossings ¶
    • depends_on definition 11.96 Local, global, trials factor ¶ ↺
  • depends_on lemma 11.50 Markov and Chebyshev inequalities ¶ ↺
  • depends_on theorem 7.23 Intermediate value theorem ¶
    • depends_on axiom 7.1 Completeness of $\R$ ¶
    • depends_on definition 7.20 Continuity at a point ¶
      • depends_on definition 7.16 Limit ¶
        • depends_on definition 7.2 Absolute value ¶
        • depends_on definition 7.9 Real function ¶
      • depends_on equation 7.7 eq:ana-limit-left ¶
      • depends_on equation 7.5 eq:ana-limit-right ¶
    • proves proof ch:05-real-analysis@proof-8 ¶
  • proves proof ch:09-probability-statistics@proof-44 ¶
• depends_on theorem 11.103 Level dependence of the mean upcrossing count ¶
  • depends_on definition 11.100 Upcrossings ¶ ↺
  • depends_on theorem 11.102 Rice's formula ¶
    • depends_on definition 11.28 Gaussian distribution ¶
      • depends_on definition 11.20 Density ¶ ↺
    • depends_on definition 11.100 Upcrossings ¶ ↺
    • proves proof ch:09-probability-statistics@prooflink-5 ¶
  • proves proof ch:09-probability-statistics@proof-45 ¶

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