biased but consistent estimator example 0. But the rate at which they converge may be quite different. An estimator can be unbiased but not consistent. For example the OLS estimator is such that (under some assumptions): meaning that it is consistent, since when we increase the number of observation the estimate we will get is very close to the parameter (or the chance that the difference between the estimate and the parameter is large (larger than epsilon) is zero). For example, if the mean is estimated by ∑ + it is biased, but as → ∞, it approaches the correct value, and so it is consistent. Practice: Biased and unbiased estimators. Let us show this using an example. Now we can compare estimators and select the “best” one. More details. Your estimator x ~ = x 1 is unbiased as E (x ~) = E (x 1) = μ implies the expected value of the estimator equals the population mean. An estimator which is not unbiased is said to be biased. 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