Which of the following statements are not true?
A) Maximizing the likelihood function gives the parameter values for which the observed sample is most likely to have been generated---that is, the parameter values that "agree most likely" with the observed data.
B) Different principles of estimation may yield different estimators of the unknown parameters.
C) The maximum likelihood estimator of the population standard deviation $\sigma$
Is the sample standard deviation S.
D) None of the above statements are true.

Question

Quizplus · Accepted Answer

The maximum likelihood estimator (MLE) for the population standard deviation $\sigma$ in a normal distribution is not exactly the sample standard deviation $S$, but rather a biased estimator. The unbiased estimator of the population variance ($\sigma^2$) involves dividing by $n-1$ (degrees of freedom) rather than $n$, which is what differentiates the sample standard deviation from the MLE of $\sigma$.

Which of the Following Statements Are Not True? A) Maximizing σ\sigmaσ

Which of the Following Statements Are Not True?
A) Maximizing $\sigma$