Question

advanced estimation theory.pdf 9/25 4 Find a consistent estimator of 2, where E(Y) = /i is the population mean and Y, is the sample mean. If E(Y2) = 2 then prove that -1 Y2 is an consistent estimator of uh u 1 Y2 - Y2 is a consistent 3 We define o2 = - /u2. Show that estimator of o2. S2 O Show that hence, S2 is a consistent estimator of o2 Takeaway S2 is not an unbiased estimator for o2 for small sample but for it is a consistent estimator of o2.

Find a consistent estimator of µ 2 , where E(Y ) = µ is the population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) = µ 0 2 then prove that 1 n Pn i=1 Y 2 i is an consistent estimator of µ 0 2 3 We define σ 2 = µ 0 2 − µ 2 . Show that S 2 n = 1 n Pn i=1 Y 2 i − Y¯ 2 n is a consistent estimator of σ 2 . 4 Show that hence, S 2 is a consistent estimator of σ 2 .

WITH EXPLANATION PLSS

Answer 1

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