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Topic: covariance
Replies: 1   Last Post: Mar 7, 2010 10:42 AM

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Jack Tomsky

Posts: 1,835
Registered: 12/18/04
Re: covariance
Posted: Mar 7, 2010 10:42 AM
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> In statistics the sample variance is different from
> population
> variance, is it the same for sample covariance? Do we
> divide by n-1
> instead of n?

Let NUM = Sum(Xik-XBARi)(Xjk-XBARj) be the numerator, where the sum is over k = 1, ..., n.

1). The unbiased estimate of the covariance, SIGij, is NUM/(n-1).

2). For samples from a multivariate normal distribution, the maximum likelihood estimate of SIGij is NUM/n.

3). For samples from a multivariate normal distribution, the minimum mean-square estimate of SIGij is NUM/(n+1).


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