Category:Gujarati -> Chapter 05
Question:
05.17 Let . A random sample of three observations was obtained from this population. Consider the following estimators of μx:

                 

a. Is û1 an unbiased estimator of μx? What about û2?
b. If both estimators are unbiased, which one would you choose? (Hint: Compare the variances of the two estimators.)
c. [my adds] What does it mean for an estimator to be “unbiased?” What is the practical acid-test?
d. Which MS Excel variance function returns an unbiased sample variance; =VARP(), =VAR() or =VAR()*(n-1)/n?
e. Are OLS estimators (e.g., slope, intercept) unbiased?
f. Are BLUE estimators unbiased?

Answers:

05.17 a.

Hence it is an unbiased estimator. Similarly, it can be shown that û2 is also unbiased.

05.17 b.

c. [my adds] What does it mean for an estimator to be “unbiased?” What is the practical acid-test?
Unbiased: the expected value (the average value) of the estimator equals the population parameter.
Because unbiasedness is a “repeated sampling property,” it is proven by repeated samping: as we increase the number of samples, the average sample estimate will converge on the population parameter (if the estimator is unbiased). (note: estimator is the recipe/formula that produces the estimate value)

d. Which MS Excel variance function returns an unbiased sample variance; =VARP(), =VAR() or =VAR()*(n-1)/n?
VAR() returns the unbiased sample variance because it is the sum of squared deviations divided by (n-1)
Dividing by (n) returns the population variance or the MLE estimator.

e. Are OLS estimators (e.g., slope, intercept) unbiased?
Yes.

f. Are BLUE estimators unbiased?
Yes, the “U” in BLUE refers to unbiased.

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