Statistical Inference

Question 1

What is the name of the method that is based on the idea that sample moments should provide good estimates of the corresponding population moments?

Answer 1

Method of Moments

Question 2

What is the term for an estimator that converges toward the parameter being estimated as the sample size increases?

Answer 2

Consistent

Question 3

What is the formula for the mean square error (MSE) of an estimator ?

Answer 3

MSE( ) = Var( ) + [Bias( )]^2

Question 4

What is the ratio మ భ used for when comparing two estimators?

Answer 4

Relative efficiency

Question 5

What is the law of large numbers?

Answer 5

It is the property that states that the sample mean is a consistent estimator for the mean of the population

Question 6

What is the difference between descriptive and inferential statistics?

Answer 6

Descriptive statistics is the branch of statistics that collects, summarizes and describes data. Inferential statistics is the branch of statistics that draws conclusions and makes decisions based on data.

Question 7

What is an unbiased estimator?

Answer 7

An unbiased estimator is a statistic that has an expected value equal to the parameter it estimates. For example, the sample mean is an unbiased estimator of the population mean.

Question 8

What is the law of large numbers?

Answer 8

The law of large numbers is a theorem that states that as the sample size increases, the sample mean converges to the population mean with probability one. In other words, the sample mean becomes more accurate as more data is collected.

Question 9

What does it mean for an estimator to be unbiased?

Answer 9

An estimator is unbiased if its expected value is equal to the true value of the parameter.

Question 10

What does it mean for an estimator to be efficient?

Answer 10

An estimator is efficient if it has the smallest variance among all unbiased estimators of the same parameter.