statistics !!

Question

1) An unbiased estimator will have a value, on average across samples, equal to the population parameter value.

Correct or Incorrect?

2) MAD is the summation of the residuals divided by the sample size.

Correct or Incorrect ?

3) The difference between expected payoff under certainty and expected value of the best act without certainty is the :

expected monetary value

expected net present value

expected value of perfect information

expected rate of return

Answer 1

最愛解答

1: Absolutely INCORRECT. Wrong concept.

Normally, we don’t know the distribution of the population, and other population properties (e.g. population mean, standard deviation, skewness, kurtosis, etc.)

As a result, we take some samples from the population for study. Sample mean and sample variance are evaluated. However, we could NOT claim that sample mean = population mean.

We could prove theoretically that sample mean (= Sx / n) is an unbiased estimator of population mean. That’s E(Sx / n) = population mean when the sample size n goes to infinity or goes to the finite population size. Obviously, if sample size = population size, sample must be equal to the population mean.

The main point is sample size always smaller than the population size. We could not make any definite statement that the sample mean is equal (or not equal) to the population mean. Sample mean is just an unbiased estimator of the population mean.

E.g.: for an unbiased dice, the population mean (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5

Now, if we take 1 sample from the dice, it could not be equal to 3.5. However, if we take 1000 (or other large nos.) samples from the dice, the average outcome would converge (not equal) to 3.5. Actually, you could still work out a variance for the sample mean (not sample variance). Hence, you could know that, even sample mean is not a constant (sample means for 1-1000 samples and for 1001-2000 samples may not be the same).

2010-03-31 15:44:21 補充：

for question 2 & 3, please provide some background information

Answer 2

why is incorrrect for MAD question?

Answer 3

1 Correct

2 Incorrect MAD means mean or median absolute deviation

3 expected value of perfect information

2010-03-31 16:29:21 補充：

1 is correct. Since there is a sentense "on average across samples". It indicates the concept that E(X_bar)=μ.