Keyword Analysis & Research: consistency of variance estimator


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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.

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