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?
--------------------------------------------------------
> 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
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