For a biased estimator θˆ of θ, which one is correct_______________?
Correct answer: B. MSE(θˆ)=Var(θˆ)+Bias2
- A. MSE(θˆ)=SD(θˆ)+Bias
- B. MSE(θˆ)=Var(θˆ)+Bias2
- C. MSE(θˆ)=SD(θˆ)+Bias2
- D. MSE(θˆ)=Var(θˆ)+Bias
Explanation
The mean squared error decomposes into variance plus squared bias: MSE(θ̂)=Var(θ̂)+[Bias(θ̂)]². Bias itself may be positive or negative, so it cannot be added without squaring.
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