Which of the following statements are not always true?
A) A point estimator $\hat { \theta }$
Is said to be an unbiased estimator of parameter $\theta$
If $E ( \hat { \theta } ) = \theta$
For every possible value of $\theta$
)
B) If the estimator $\hat { \theta }$
Is not unbiased of parameter $\theta$
, the difference $E ( \hat { \theta } ) - \theta$
Is called the bias of $\hat { \theta }$
)
C) A point estimator $\hat { \theta }$
Is unbiased if its probability sampling distribution is always "centered" at the true value of the parameter $\theta$
, where "centered" here means that the median of the distribution of $\hat { \theta } \text { is } \theta$
)
D) All of the above statements are true.

Question

Quizplus · Accepted Answer

Statement C is not always true because an unbiased estimator is defined as one where the expected value $E(\hat{\theta})$ equals the parameter $\theta$, not necessarily that the median of its sampling distribution is $\theta$. The concept of being "centered" at $\theta$ typically refers to the mean (expected value) rather than the median.

Which of the Following Statements Are Not Always True? A) θ^\hat { \theta }θ^

Which of the Following Statements Are Not Always True?
A) $\hat { \theta }$