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Under linear loss, the Bayes estimate of 𝜃 is the sum of 𝑘0 and 𝑘1
Under linear loss, the Bayes estimate of 𝜃 is the sum of 𝑘0 and 𝑘1
False
Absolute loss function results when 𝑘0 = 𝑘1 = 1
Absolute loss function results when 𝑘0 = 𝑘1 = 1
True
Asymmetric linear loss results when 𝑘0 = 𝑘1
Asymmetric linear loss results when 𝑘0 = 𝑘1
False
The Bayes estimate under linear loss is the solution to the equation 𝑙(𝜃, 𝜃෨) = ൝ 𝑘0𝜃 - 𝜃෨ , 𝑘1𝜃෨ - 𝜃 if 𝜃෨ < 𝜃 if 𝜃෨ ≥ 𝜃
The Bayes estimate under linear loss is the solution to the equation 𝑙(𝜃, 𝜃෨) = ൝ 𝑘0𝜃 - 𝜃෨ , 𝑘1𝜃෨ - 𝜃 if 𝜃෨ < 𝜃 if 𝜃෨ ≥ 𝜃
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The posterior expected loss is independent of the values of 𝑘0 and 𝑘1
The posterior expected loss is independent of the values of 𝑘0 and 𝑘1
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When 𝜃෨ is greater than or equal to 𝜃, the linear loss function is not defined
When 𝜃෨ is greater than or equal to 𝜃, the linear loss function is not defined
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The Bayes estimate under linear loss involves calculating the posterior expected loss
The Bayes estimate under linear loss involves calculating the posterior expected loss
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The solution to the linear loss equation depends on finding the quantile of a probability distribution
The solution to the linear loss equation depends on finding the quantile of a probability distribution
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In the asymmetric linear loss function, the coefficients 𝑘0 and 𝑘1 must be equal
In the asymmetric linear loss function, the coefficients 𝑘0 and 𝑘1 must be equal
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The linear loss function simplifies to the absolute loss function when 𝑘0 ≠ 1 and 𝑘1 = 1
The linear loss function simplifies to the absolute loss function when 𝑘0 ≠ 1 and 𝑘1 = 1
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