# Keyword Analysis & Research: consistency of variance estimator

## Keyword Research: People who searched consistency of variance estimator also searched

Is the sample variance estimator strongly consistent?

Now, it is widely known that this sample variance estimator is simply consistent (convergence in probability). I wonder, is it also true that it is strongly consistent, i.e. it converges to population variance almost surely? And if yes, are there any additional requirements for { X n } n ≥ 1? terrytao.wordpress.com/2008/06/18/…

What is variance estimation?

Variance estimation is a statistical inference problem in which a sample is used to produce a point estimate of the variance of an unknown distribution. The problem is typically solved by using the sample variance as an estimator of the population variance. IID samples from a normal distribution whose mean is unknown.

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.

What is the variance of an unbiased estimator?

In particular, for an unbiased estimator, the variance equals the MSE. . A consistent sequence of estimators is a sequence of estimators that converge in probability to the quantity being estimated as the index (usually the sample size) grows without bound.