Question: Substituting asymptotically unbiased for unbiased in Theorem 10 3 show
Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, show that X + 1 / n+ 2 is a consistent estimator of the binomial parameter θ.
Answer to relevant QuestionsUse the result of Example 8.4 on page 253 to show that for random samples of size n = 3 the median is a biased estimator of the parameter θ of an exponential population. In reference to Exercise 10.43, is X1 + 2X2 / n1 + 2n2 a sufficient estimator of θ? Given a random sample of size n from a beta population with β = 1, use the method of moments to find a formula for estimating the parameter α. Given a random sample of size n from a normal population with the known mean µ, find the maximum likelihood estimator for σ. If V1, V2, . . . , Vn and W1, W2, . . . , Wn are independent random samples of size n from normal populations with the means µ1 = α + β and µ2 = α – β and the common variance σ2 = 1, find maximum likelihood ...
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