Mathematics · Mathematical Statistics
Let X1, X2, ..., Xn (n ≥ 3) be a random sample from the uniform distribution on the interval (θ1 - θ2, θ1 + θ2), where θ1 ∈ R and θ2 > 0 are unknown parameters. Let X(j) be the jth order statistic, and let X̄ be the sample mean. If (X(1), X(n)) is a complete and sufficient statistic for (θ1, θ2), which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(n(X(n) - X(1)))/(2(n-1)) is the uniformly minimum variance unbiased estimator (UMVUE) of θ2
- 2(X(1) + X(n))/2 is the uniformly minimum variance unbiased estimator (UMVUE) of θ1✓
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Correct answer
(X(1) + X(n))/2 is the uniformly minimum variance unbiased estimator (UMVUE) of θ1
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