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日期：2021-11-12
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  • 00:00 1.
    Large Sample Theory And Maximum Likelihood Estimator
  • 00:28 2.
    Convergence
  • 19:57 3.
    Their Relationship
  • 20:38 4.
    Useful Results
  • 26:06 5.
    Useful Results
  • 26:29 6.
    Law of Large Number
  • 36:06 7.
    Proof of LLN 1
  • 37:10 8.
    Condition for Consistency
  • 37:11 9.
    Proof of LLN 1
  • 37:13 10.
    Law of Large Number
  • 37:20 11.
    Proof of LLN 1
  • 37:26 12.
    Condition for Consistency
  • 37:54 13.
    Consistency of LS Estimator
  • 47:30 14.
    Ex. 4-2: 𝑠 2 = 𝑡=1 𝑇 𝑥 𝑡 − 𝑥 2 𝑇−1 → 𝜎 2 ?
  • 47:33 15.
    LLN vs. CLT
  • 47:35 16.
    Ex. 4-2: 𝑠 2 = 𝑡=1 𝑇 𝑥 𝑡 − 𝑥 2 𝑇−1 → 𝜎 2 ?
  • 47:35 17.
    Consistency of LS Estimator
  • 47:38 18.
    Ex. 4-2: 𝑠 2 = 𝑡=1 𝑇 𝑥 𝑡 − 𝑥 2 𝑇−1 → 𝜎 2 ?
  • 47:39 19.
    LLN vs. CLT
  • 52:04 20.
    LLN vs. CLT
  • 57:09 21.
    Central Limit Theorem
  • 58:20 22.
    Ex. 4-3: The Asymptotical Distribution of 𝑇 𝑏
  • 59:41 23.
    Maximum Likelihood Estimation
  • 1:14:55 24.
    Solving for MLE
  • 1:17:10 25.
    MLE Examples
  • 1:23:11 26.
    MLE Examples
  • 1:23:16 27.
    Properties of MLE
  • 1:23:18 28.
    MLE Examples
  • 1:24:03 29.
    Properties of MLE
  • 1:43:47 30.
    Properties of MLE
  • 1:44:05 31.
    Lemma 4-2:
  • 1:44:56 32.
    A) MLE are consistent. 𝜃 𝑛→∞ 𝜃
  • 1:48:13 33.
    B) MLE are Asymptotic Normal
  • 1:49:40 34.
    Ex. 4-4: Poisson Distribution
  • 1:51:51 35.
    Ex. 4-4 MLE Example: Poisson
  • 1:53:52 36.
    4-5 MLE Example: Bernoulli
  • 1:56:25 37.
    Ex. 4-5: 𝑋~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑤𝑖𝑡ℎ 𝑝
  • 1:56:33 38.
    4-5 MLE Example: Bernoulli
  • 1:56:54 39.
    Ex. 4-5: 𝑋~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑤𝑖𝑡ℎ 𝑝
  • 2:00:30 40.
    Cramer Rao Bound: The Variance of An Unbiased Estimator is no smaller than −𝐄(𝐇) −𝟏
  • 2:00:41 41.
    Ex. 4-5: 𝑋~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑤𝑖𝑡ℎ 𝑝
  • 2:00:43 42.
    Cramer Rao Bound: The Variance of An Unbiased Estimator is no smaller than −𝐄(𝐇) −𝟏
  • 2:03:20 43.
    The Invariance Principle
  • 2:06:21 44.
    Tests Based on MLE
  • 2:09:01 45.
    Tests Based on MLE
  • 2:09:06 46.
    Estimation of Variance of MLE
  • 2:09:09 47.
    Ex. Test, Poisson Distribution
  • 2:09:12 48.
    Ex. Test, Poisson Distribution
  • 2:09:14 49.
    Ex. Test, Poisson Distribution
  • 2:09:17 50.
    Ex. Test, Poisson Distribution
  • 2:09:18 51.
    To Compute LMT
  • 2:09:19 52.
    Ex. 4-6 Normal Distribution
  • 2:09:50 53.
    Example: Normal Distribution
  • 2:12:24 54.
    Example: Normal Distribution
  • 2:13:46 55.
    Example: Normal Distribution
  • 2:13:54 56.
    Example: Normal Distribution
  • 2:13:54 57.
    Example: Normal Distribution
  • 2:14:02 58.
    Example: Normal Distribution
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metrics-4-Large Sample Theory and MLE-20211105
長度: 2:22:33, 瀏覽: 604, 最近修訂: 2021-11-12
    下一篇
    • 00:00 1.
      Large Sample Theory And Maximum Likelihood Estimator
    • 00:28 2.
      Convergence
    • 19:57 3.
      Their Relationship
    • 20:38 4.
      Useful Results
    • 26:06 5.
      Useful Results
    • 26:29 6.
      Law of Large Number
    • 36:06 7.
      Proof of LLN 1
    • 37:10 8.
      Condition for Consistency
    • 37:11 9.
      Proof of LLN 1
    • 37:13 10.
      Law of Large Number
    • 37:20 11.
      Proof of LLN 1
    • 37:26 12.
      Condition for Consistency
    • 37:54 13.
      Consistency of LS Estimator
    • 47:30 14.
      Ex. 4-2: 𝑠 2 = 𝑡=1 𝑇 𝑥 𝑡 − 𝑥 2 𝑇−1 → 𝜎 2 ?
    • 47:33 15.
      LLN vs. CLT
    • 47:35 16.
      Ex. 4-2: 𝑠 2 = 𝑡=1 𝑇 𝑥 𝑡 − 𝑥 2 𝑇−1 → 𝜎 2 ?
    • 47:35 17.
      Consistency of LS Estimator
    • 47:38 18.
      Ex. 4-2: 𝑠 2 = 𝑡=1 𝑇 𝑥 𝑡 − 𝑥 2 𝑇−1 → 𝜎 2 ?
    • 47:39 19.
      LLN vs. CLT
    • 52:04 20.
      LLN vs. CLT
    • 57:09 21.
      Central Limit Theorem
    • 58:20 22.
      Ex. 4-3: The Asymptotical Distribution of 𝑇 𝑏
    • 59:41 23.
      Maximum Likelihood Estimation
    • 1:14:55 24.
      Solving for MLE
    • 1:17:10 25.
      MLE Examples
    • 1:23:11 26.
      MLE Examples
    • 1:23:16 27.
      Properties of MLE
    • 1:23:18 28.
      MLE Examples
    • 1:24:03 29.
      Properties of MLE
    • 1:43:47 30.
      Properties of MLE
    • 1:44:05 31.
      Lemma 4-2:
    • 1:44:56 32.
      A) MLE are consistent. 𝜃 𝑛→∞ 𝜃
    • 1:48:13 33.
      B) MLE are Asymptotic Normal
    • 1:49:40 34.
      Ex. 4-4: Poisson Distribution
    • 1:51:51 35.
      Ex. 4-4 MLE Example: Poisson
    • 1:53:52 36.
      4-5 MLE Example: Bernoulli
    • 1:56:25 37.
      Ex. 4-5: 𝑋~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑤𝑖𝑡ℎ 𝑝
    • 1:56:33 38.
      4-5 MLE Example: Bernoulli
    • 1:56:54 39.
      Ex. 4-5: 𝑋~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑤𝑖𝑡ℎ 𝑝
    • 2:00:30 40.
      Cramer Rao Bound: The Variance of An Unbiased Estimator is no smaller than −𝐄(𝐇) −𝟏
    • 2:00:41 41.
      Ex. 4-5: 𝑋~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑤𝑖𝑡ℎ 𝑝
    • 2:00:43 42.
      Cramer Rao Bound: The Variance of An Unbiased Estimator is no smaller than −𝐄(𝐇) −𝟏
    • 2:03:20 43.
      The Invariance Principle
    • 2:06:21 44.
      Tests Based on MLE
    • 2:09:01 45.
      Tests Based on MLE
    • 2:09:06 46.
      Estimation of Variance of MLE
    • 2:09:09 47.
      Ex. Test, Poisson Distribution
    • 2:09:12 48.
      Ex. Test, Poisson Distribution
    • 2:09:14 49.
      Ex. Test, Poisson Distribution
    • 2:09:17 50.
      Ex. Test, Poisson Distribution
    • 2:09:18 51.
      To Compute LMT
    • 2:09:19 52.
      Ex. 4-6 Normal Distribution
    • 2:09:50 53.
      Example: Normal Distribution
    • 2:12:24 54.
      Example: Normal Distribution
    • 2:13:46 55.
      Example: Normal Distribution
    • 2:13:54 56.
      Example: Normal Distribution
    • 2:13:54 57.
      Example: Normal Distribution
    • 2:14:02 58.
      Example: Normal Distribution
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