Mathematics · Statistical Inference
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, j = 1, 2, ..., n, and let X_bar = 1n ∑ Xi. Here, (X(1), X(n)) is a complete and sufficient statistic for (θ1, θ2). Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(n + 1)(X(n) - X(1))2(n - 1) is a biased estimator of θ2
- 2X(1) + X(n)2 is the uniformly minimum variance unbiased estimator of θ1✓
- 3(X_bar - X(1)) is an unbiased estimator of θ2
- 4X_bar is a biased estimator of θ1
Correct answer
X(1) + X(n)2 is the uniformly minimum variance unbiased estimator of θ1
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