remark 11.90 Failure I: a parameter on the boundary

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 definition 11.59 Regularity conditions ¶ ↺

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