Question: If 1 and 2 are independent unbiased estimators of a
If Θ1 and Θ2 are independent unbiased estimators of a given parameter θ and var(Θ1) = 3 ∙ var(Θ2), find the constants a1 and a2 such that a1Θ1 + a2Θ2 is an unbiased estimator with minimum variance for such a linear combination.
Answer to relevant QuestionsShow that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter θ. With reference to Exercise 10.21, find the efficiency of the estimator of part (a) with ω = 1/2 relative to this estimator with In exercise If 1 is the mean of a random sample of size n from a normal population with the ...With reference to Exercise 10.12, show that 2X – 1 is also an unbiased estimator of k, and find the efficiency of this estimator relative to the one of part (b) of Exercise 10.12 for (a) n = 2; (b) n = 3. Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, show that X + 1 / n+ 2 is a consistent estimator of the binomial parameter θ. If X1, X2, and X3 constitute a random sample of size n = 3 from a Bernoulli population, show that Y = X1 + 2X2 + X3 is not a sufficient estimator of θ. Consider special values of X1, X2, and X3.)
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