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# 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 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 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
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. Set up payoff table Actions States of Nature Actions High Success Moderate Success Unsucc- essful Min Payoff New 130,000 60,000 -10,000 -10,000 Old 30,000 70,000 90,000 30,000 Therefore, Maximin Criterion would select Old Actions Regrets or Opportunity Loss Table Actions High Success Moderate Success Unsucc- essful Max Regrets New 0 10,000 40,000 40,000 Old 100,000 0 0 100,000 Therefore, Minimax Regrets Criterion selects Old b. Therefore, Maximin Criterion would select Old c. Therefore, Minimax Regrets Criterion selects Old 19.10 a.

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ismch19 - Chapter 19 Statistical Decision Theory 149...

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