Which of the following statements are true?
A) Maximizing the likelihood estimation is the most widely used estimation technique among statisticians.
B) Under very general conditions on the joint distribution of the sample, when the sample size n is large, the maximum likelihood estimator of any parameter $\theta$
Is approximately unbiased; that is, $E ( \hat { \theta } ) \approx \theta$
)
C) Under very general conditions on the joint distribution of the sample, when the sample size n is large, the maximum likelihood estimator of any parameter $\theta$
Has variance, is nearly as small as small as can be achieved by any estimator.
D) In recent years, statisticians have proposed an estimator, called an M-estimator, which is based on a generalization of maximum likelihood estimation.
E) All of the above are true statements.

Question

Quizplus · Accepted Answer

All of the statements are true. A) Maximum likelihood estimation is indeed a widely used technique for estimating the parameters of a statistical model. B) Under general conditions, maximum likelihood estimators are approximately unbiased when the sample size is large. C) They also have a variance that is nearly as small as any estimator could achieve under similar conditions, making them efficient. D) M-estimators are a generalization of maximum likelihood estimators, expanding the types of problems and models that can be addressed.

Which of the Following Statements Are True? A) Maximizing the Likelihood

Which of the Following Statements Are True?
A) Maximizing the Likelihood