No, not all unbiased estimators are consistent. Let us show this using an example. 2 is more efficient than 1.

Example 4. Say an exponential distribution with parameter 1 since expectation of the estimator given here is 1. Suppose we are trying to estimate [math]1[/math] by the following procedure: [math]X_i[/math]s are drawn from the set [math]\{-1, 1\}[/math]. θ If an estimator is not an unbiased estimator, then it is a biased estimator.

The current example does not seem to be quite right. Example of Unbiased Estimator that is not Consistent. 1: Unbiased and consistent 2: Biased but consistent 3: Biased and also not consistent 4: Unbiased but not consistent (1) In general, if the estimator is unbiased, it is most likely to be consistent and I had to look for a specific hypothetical example for when this is … Value of Estimator . These are all illustrated below. One such case is when a plus four confidence interval is used to construct a confidence interval for a population proportion. 2. I have some troubles with understanding of this explanation taken from wikipedia: "An estimator can be unbiased but not consistent. If X 1;:::;X nform a simple random sample with unknown finite mean , then X is an unbiased estimator of . This satisfies the first condition of consistency. Efficiency .
Further, mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is (see § Effect of transformations); for example, the sample variance is a biased estimator for the population variance, but its square root, the sample standard deviation, is an unbiased estimator for the population standard deviation. Just because an iid sample is chosen x(1) cannot be unbiased. Example: Show that the sample mean is a consistent estimator of the population mean.


If the X ihave variance ˙2, then Var(X ) = ˙2 n: In the methods of moments estimation, we have used g(X ) as an estimator for g( ). Although a biased estimator does not have a good alignment of its expected value with its parameter, there are many practical instances when a biased estimator can be useful. I think a more specific example is required. Example: Three different estimators’ distributions – 1 and 2: expected value = population parameter (unbiased) – 3: positive biased – Variance decreases from 1, to 2, to 3 (3 is the smallest) – 3 can have the smallest MST.

1. If gis a convex function, we can say something about the bias of this estimator. 1, 2, 3 based on samples of the same size . uas an estimator for ˙is downwardly biased. 3. Example for … Solution: We have already seen in the previous example that $$\overline X $$ is an unbiased estimator of population mean $$\mu $$.