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 <[EMAIL PROTECTED]> wrote: > > Michael <[EMAIL PROTECTED]> 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]] > > > > ______________________________________________ > > [email protected] mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > > > > -- > 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 > ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) > 35327907 > [[alternative HTML version deleted]]
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