theorem A.214 Wilks, $k$ parameters and $r$ constraints

Rests on

• depends_on lemma A.213 The three minima ¶
  • depends_on corollary A.210 Uniform quadratic approximation on the $n^{-1/2}$ scale ¶
    • depends_on lemma A.208 The three averages ¶
      • 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 theorem A.206 Cramér–Wold, and continuous mapping ¶
        • depends_on definition 11.21 Distribution function ¶
        • depends_on lemma 11.52 Slutsky ¶
      • depends_on theorem A.205 Weak law under integrability alone ¶
        • depends_on corollary 11.51 Weak law of large numbers ¶
      • proves proof app:A-long-proofs@proof-126 ¶
    • depends_on lemma A.209 Uniform third-order remainder ¶
      • depends_on definition 11.59 Regularity conditions ¶ ↺
      • depends_on theorem 7.38 Taylor's theorem with Lagrange remainder ¶
        • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on theorem 7.34 Rolle ¶
        • proves proof ch:05-real-analysis@proof-22 ¶
      • proves proof app:A-long-proofs@proof-127 ¶
    • proves proof app:A-long-proofs@proof-128 ¶
  • depends_on lemma A.212 Second-order flatness ¶
    • depends_on definition A.203 The constraint surface ¶
      • 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 theorem 7.38 Taylor's theorem with Lagrange remainder ¶ ↺
    • proves proof app:A-long-proofs@proof-130 ¶
  • depends_on lemma A.211 Root-$n$ localisation ¶
    • depends_on lemma A.208 The three averages ¶ ↺
    • depends_on lemma A.209 Uniform third-order remainder ¶ ↺
    • proves proof app:A-long-proofs@proof-129 ¶
  • proves proof app:A-long-proofs@proof-131 ¶
• 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 theorem A.206 Cramér–Wold, and continuous mapping ¶ ↺
• proves proof app:A-long-proofs@proof-132 ¶

Supports

Nothing declares a dependency on this node yet.