Find the probability limits of w1 and w2

Reference no: EM13178866

Let Y denote the sample average from a random sample with mean ? and variance ? 2. Consider two alternative estimators of ?: W1 =((n- 1)/n)Y and W2= Y /2.

(a) Show that W1 and W2 are both biased estimators of ? and find the biases. What happens to the biases as n tends to infinity. Comment on any important differences in the bias for the estimators as n tends to infinity.

(b) Find the probability limits of W1 and W2. State whether these estimators are consistent or inconsistent.

(d) Argue that W1 is a better estimator than Y if ? is "close" to zero for any value of n. (Hint: Compare the Mean Square Errors of W1 and Y )

Reference no: EM13178866

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