Question: A statistician has to decide on the basis of a
A statistician has to decide on the basis of a single observation whether the parameter θ of the density
Equals θ1 or θ2, where θ1 < θ2. If he decides on θ1 when the observed value is less than the constant k, on θ2 when the observed value is greater than or equal to the constant k, and he is fined C dollars for making the wrong decision, which value of k will minimize the maximum risk?
Answer to relevant QuestionsFind the value of θ that maximizes the risk function of Example 9.8, and then find the values of a and b that minimize the risk function for that value of θ. Compare the results with those given on page 272. If X1, X2, . . . , Xn constitute a random sample from a normal population with µ = 0, show that Is an unbiased estimator of σ2. Show that for the unbiased estimator of Example 10.4, n + 1 / n ∙ Yn, the Cramer-Rao inequality is not satisfied. If X1 and X2 constitute a random sample of size n = 2 from an exponential population, find the efficiency of 2Y1 relative to , where Y1 is the first order statistic and 2Y1 and are both unbiased estimators of the ...With reference to Exercise 10.33, use Theorem 10.3 to show that Y1 – 1/n+1 is a consistent estimator of the parameter α.
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