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 ______________________________________________ [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
