ismch19 - Chapter 19 Statistical Decision Theory 149...

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Chapter 19: Statistical Decision Theory 149 Chapter 19: Statistical Decision Theory 19-1 No, all actions are admissible 19-2 D is dominated by C. Therefore, D is inadmissible. 19-3 a. The Maximin criterion would select the Certificate of Deposit: Actions States of Nature Investment Alternatives S1 S2 S3 Minimum Payoff Certificate of Deposit 1200 1200 1200 1200 Low-risk stock fund 4300 1200 -600 -600 High-risk stock fund 6600 800 -1500 -1500 b. The Minimax regret criteria would select the Low-risk stock fund: Actions States of Nature Investment Alternatives S1 S2 S3 Maximum Regret Certificate of Deposit 5400 0 0 5400 Low-risk stock fund 2300 0 1800 2300 High-risk stock fund 0 400 2700 2700 19.4 a. Note – D is dominated by C. Hence D is inadmissible Maximin criterion would select production process C: Actions States of Nature Prod. Process Low Demand Moderate Demand High Demand Min Payoff A 100,000 350,000 900,000 100,000 B 150,000 400,000 700,000 150,000 C 250,000 400,000 600,000 250,000
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150 th Edition b. Minimax regret criterion would select production process A: Actions States of Nature Prod. Process Low Demand Moderate Demand High Demand Max Regret A 150,000 50,000 0 150,000 B 100,000 0 200,000 200,000 C 0 0 300,000 300,000 19.5 a. Maximax criterion would select production process A with a payoff of 200,000 b. Maximax criterion would select the stock portfolio with a 2500 payoff 19-6 Actions States of Nature Prod. Process Low Demand Moderate Demand High Demand Min Payoff A 70,000 120,000 200,000 70,000 B 80,000 120,000 180,000 80,000 C 100,000 125,000 160,000 100,000 D* 100,000 120,000 150,000 Inadmissible E 60,000 115,000 220,000 60,000 *inadmissible Therefore, production process C would be chosen using the Maximin Criterion Actions Regrets or Opportunity Loss Table Prod. Process Low Demand Moderate Demand High Demand Max Regret A 30,000 5,000 20,000 30,000 B 20,000 5,000 40,000 40,000 C 0 0 60,000 60,000 D* 0 5,000 70,000 Inadmissible E 40,000 10,000 0 40,000 *inadmissible Therefore, production process A would be chosen using the Minimax Regret Criterion 19-7 a. Payoff table where the same action is chosen under both criterion Actions States of Nature Actions S1 S2 Minimum Payoff Max Regret A1 5 5 5* 2* A2 0 7 0 5 Chose Action A1 under the Maximin criterion. Also chose Action A1 under the Minimax Regret criterion b. Different actions are chosen by the two criterion Actions States of Nature
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Chapter 19: Statistical Decision Theory 151 Actions S1 S2 Minimum Payoff Max Regret A1 5 5 5* 7 A2 0 12 0 5* Chose Action A1 under the Maximin criterion. Chose Action A2 under the Minimax Regret criterion 19.8 Assume a situation with two states of nature and two actions. Let both actions be admissible. The payoff Matrix is: Action S1 S2 A1 M 11 M 12 A2 M 21 M 22 Then action A1 will be chosen by both the Maximin and the Minimax Regret Criteria if for: M 11 > M 21 and M 12 < M 22 and (M 11 – M 21 ) > (M 22 – M 12 ) 19.9 a.
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ismch19 - Chapter 19 Statistical Decision Theory 149...

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