Q5.LetX1,X2,···Xn be an independent random sample from a distribution with ﬁnite mean µ and ﬁnite variance...

Q5.LetX1,X2,···Xn be an independent random sample from a distribution with ﬁnite mean µ and ﬁnite variance σ2. An estimator of µ in the form L = c1X1 + c2X2 +···cnXn 2 is called a linear estimator,where c1,c2,··· ,cn are some known constants.If L is unbiased,then it is called a linear unbiased estimator.A linear unbiased estimator that has the minimum variance among all linear unbiased estimators is called the best linear unbiased estimator (BLUE). (i) Express E(L) and Var(L) in terms of µ, σ2 and c1,c2,··· ,cn; (ii) Show that the sample mean is the BLUE of µ.

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TOPIC:Best linear unbiased estimator(BLUE).

orchestra answered 1 year ago

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