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## Re: Covariance Question

**From**: |
Mike Miller |

**Subject**: |
Re: Covariance Question |

**Date**: |
Sun, 2 Mar 2003 13:49:32 -0600 (CST) |

On Sun, 2 Mar 2003, Dirk Eddelbuettel wrote:
>* address@hidden:~> octave2.1 -q*
>* octave2.1:1> x=[3;1;3;9];*
>* octave2.1:2> y=[4;4;8;8];*
>* octave2.1:3> cov(x,y)*(length(x)-1)/length(x)*
>* ans = 4*
>
>* The difference depends on whether you "know" that your data comes from*
>* a sample versus a population. See e.g.*
>
>* http://newton.dep.anl.gov/newton/askasci/1993/math/MATH014.HTM*
Right. It's the N v. N-1 effect. Use of N produces the maximum
likelihood estimator for multivariate normal data. It has good properties
and is, in some ways, superior to use of N-1. That's another reason to
use N sometimes, not just because the entire population is known. Still,
N-1 is used much more often, and Octave uses N-1. I think it's the right
choice for the default behavior of the cov function. It's also what
MATLAB does.
Mike
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