Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 04 Apr 2018 My Price 6.00

probability limits

3       Let Y¯ denote the sample average from a random sample with mean m and variance 2. Consider two alternative estimators of m: W1  [(n  1)/n]Y¯ and W2 Y¯/2.

(i)    Show that W1 and W2 are both biased estimators of m and find the biases. What hap- pens to the biases as n → ? Comment on any important differences in bias for the

two estimators as the sample size gets large.

(ii)   Find the probability limits of W1 and W2. {Hint: Use Properties PLIM.1 and PLIM.2; for W1, note that plim [(n  1)/n]  1.} Which estimator is consistent?

(iii)  Find Var(W1) and Var(W2).

(iv)  Argue that W1 is a better estimator than Y¯ if m is “close” to zero. (Consider both bias

and variance.)

Answers

Maurice Tutor
(5)
Status NEW Posted 04 Apr 2018 07:04 PM My Price 6.00

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