# Keyword Analysis & Research: conditions for consistent estimator

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What is a consistent estimator?

In this way one would obtain a sequence of estimates indexed by n, and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value θ 0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent.

Can an estimator be biased but consistent?

Alternatively, an estimator can be biased but consistent. For example, if the mean is estimated by , it approaches the correct value, and so it is consistent. Important examples include the sample variance and sample standard deviation. Without Bessel's correction (that is, when using the sample size

Is an estimator consistent or asymptotically normal?

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.

Is TN a consistent estimator of?

However, T n is not a consistent estimator of μ. EDIT 3: See cardinal's points in the comments below. @G.JayKerns Unbiasedness is unnecessary for this. Consider S n = 1 n − 1 ∑ i = 1 n ( X i − X n ¯) 2. S n is a biased estimator of the standard deviation yet you can use the above argument to show that it's consistent.