How to redefine cov to calculate population covariance matrix

Question

The standard cov function calculates a sample of the covariance matrix, I want to have a covariance matrix of the population.

I tried the following:

 cov.pop <- function(x,y=NULL) { cov(x,y)*(length(x)-1)/length(x) } > sapply(list(Apple,HP,Microsoft),cov.pop,y=Apple) #correct [1] 0.7861672 0.1363396 0.2223303 > sapply(list(Apple,HP,Microsoft),cov.pop,y=HP) #correct [1] 0.13633964 0.09560376 0.05226032 > sapply(list(Apple,HP,Microsoft),cov.pop,y=Microsoft) #correct [1] 0.22233028 0.05226032 0.13519964 > cov.pop(cbind(Apple,HP,Microsoft)) #not correct Apple HP Microsoft Apple 0.8444018 0.14643887 0.23879919 HP 0.1464389 0.10268552 0.05613145 Microsoft 0.2387992 0.05613145 0.14521443 

My question
Is there an easy way to change the cov.pop function to get the correct covariance matrix of the population?

Answer 1

I think the results are different, because length in matrix (i.e. cbind(Apple, HP, Microsoft) and length in each list element does not match

 cov.pop <- function(x,y=NULL) { cov(x,y)*(NROW(x)-1)/NROW(x) } 

Using an example dataset

 set.seed(24) Apple <- rnorm(140) HP <- rnorm(140) Microsoft <- rnorm(140) cov.pop(cbind(Apple,HP,Microsoft)) # Apple HP Microsoft #Apple 0.946489639 0.006511604 0.02518080 #HP 0.006511604 1.015532869 0.04940075 #Microsoft 0.025180805 0.049400745 1.08388185 sapply(list(Apple,HP,Microsoft),cov.pop,y=Apple) #[1] 0.946489639 0.006511604 0.025180805 sapply(list(Apple,HP,Microsoft),cov.pop,y=HP) #[1] 0.006511604 1.015532869 0.049400745 sapply(list(Apple,HP,Microsoft),cov.pop,y=Microsoft) #[1] 0.02518080 0.04940075 1.08388185