For any arbitrary parameter , a biased estimator of is any estimate where:
A) the expected value of the estimate equals
B) the expected value of the estimate differs from
C) the expected value of the estimate is greater than
D) the expected value of the estimate is less than .

Question

For any arbitrary parameter  , a biased estimator of  is any estimate where:
A) the expected value of the estimate equals 
B) the expected value of the estimate differs from 
C) the expected value of the estimate is greater than 
D) the expected value of the estimate is less than .

Quizplus · Accepted Answer

A biased estimator is an estimate that is systematically too high or too low on average. In this case, we are given a specific parameter value (11eb86f3_5f69_b4e0_883a_f164b1024252_TB8195_11) and we are looking for an estimate that is biased. Options A, C, and D all mention specific values (ending in dbf1, dbf3, and dbf4) that are different from the given parameter value, so they do not meet the criteria of being an estimate of the given parameter. Option B mentions a different specific value (ending in dbf2), which means it is an estimate of a different value and could be biased either way. Therefore, the best choice is B.

For Any Arbitrary Parameter , a Biased Estimator of