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What does it mean if an estimator is inconsistent?
consistent estimator
If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent. Consistency as defined here is sometimes referred to as weak consistency.
Can an inconsistent estimator be unbiased?
“An estimator can be unbiased but not consistent. For example, for an iid sample {x1,…,xn} one can use T(X)=x1 as the estimator of the mean E[x].
Why do we need consistent estimators?
Now, to require an estimator to be consistent is to demand that it also follows this rule: As its job is to estimate an unknown parameter, we would like it to converge to that parameter (read: estimate that parameter arbitrarily well) as our sample size tends to infinity.
Which estimator is efficient?
An estimator with efficiency 1.0 is said to be an “efficient estimator”. The efficiency of a given estimator depends on the population. For example, for a normally distributed population, the sample mean is an efficient estimator of the population mean.
What does it mean when an estimator is not consistent?
An estimator which is not consistent is said to be inconsistent. You will often read that a given estimator is not only consistent but also asymptotically normal, that is, its distribution converges to a normal distribution as the sample size increases.
Which is a consistent and asymptotically normal estimator?
Consistent and asymptotically normal. You will often read that a given estimator is not only consistent but also asymptotically normal, that is, its distribution converges to a normal distribution as the sample size increases.
When do you use the locution consistent estimator?
The latter locution is often informally used to mean that 1) the same predefined rule is used to generate all the estimators in the sequence and that 2) the sequence is consistent. Thus, the concept of consistency extends from the sequence of estimators to the rule used to generate it.
When does a consistent estimator converge to a normal distribution?
You will often read that a given estimator is not only consistent but also asymptotically normal, that is, its distribution converges to a normal distribution as the sample size increases. You might think that convergence to a normal distribution is at odds with the fact that consistency implies convergence in probability to a constant