Hi Pete,

Thanks for your help! But I don't understand your answer... could you please
elaborate more?

thanks,

M

On 10 Mar 2006 09:32:12 +0100, Peter Dalgaard <p.dalgaard@biostat.ku.dk>
wrote:
>
> Michael <comtech.usa@gmail.com> writes:
>
> > Hi all,
> >
> > Why cov(y, y) only gives one value, and cov(t(y), t(y)) gives 3x3 NA
> matrix?
> >
> > Here my y is listed below and it is a 3x1 matrix.
> >
> > I am expecting that if I have a random vector y=[y1 y2 y3]', here " ' "
> > denotes a transposition so that
> >
> > y is a column vector, where y1, y2, y3 are independent random
> variables...
> >
> > then cov(y, y) should be
> >
> > E[ y * y' ] - E[y] * E[y] ',
> >
> > and it should generate an 3x3 identity matrix.
> >
> > In fact, as you can see, my y below is generated by
> >
> > y=[f(1)+e1, f(2)+e2, f(3)+e3]',
> >   =[ 1^2+e1, 2^2+e2, 3^2+e3]',
> >   =[ 1 + e1,  4 + e1,  9 + e1].
> > where f(x)=x^2, e1, e2, e3 are three independent normal(0, 1) sample
> > values...
> >
> > so I expect the cov(y, y) will be a 3x3 identity matrix.
> >
> > What's wrong here?
>
> Nothing.
>
> cov(X,X) ::= crossprod(scale(X,scale=FALSE))/(nrow(X)-1)
>
> if X is a matrix and same thing with  .../(length(X)-1) if X is a
> vector. Try calculating the constituent parts.
>
>
> > > cov(y, y)
> >          [,1]
> > [1,] 13.78024
> > > cov(t(y), t(y))
> >      [,1] [,2] [,3]
> > [1,]   NA   NA   NA
> > [2,]   NA   NA   NA
> > [3,]   NA   NA   NA
> > > y
> >          [,1]
> > [1,] 1.146766
> > [2,] 5.412608
> > [3,] 8.542067
> >
> >       [[alternative HTML version deleted]]
> >
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> >
>
> --
>    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
> (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45)
> 35327918
> ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)                  FAX: (+45)
> 35327907
>

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