3 Dimensional Cross Variance

["Paul Lasky" <phlasky@earthlink.net>]

This is a pretty basic question but  . . . is there a better way, without explicit looping, to compute the  3 dimensional cross variance and a diagonal ?  The crossvariance defined as:

      crossvar = array( rep( NA,  p^3 ), dim=c ( p, p, p ) )

      for( i in 1 : p )

        {

          for( j in 1 : p )

           {

             for( k in 1 : p )

              {

                crossvar[ i, j, k ] = 0.5 * t( x[ , i ] ) % * % Q[ , , k] % * % x[ , j ] 

                   }

               }

         }

where x are the  bi-variates, and Q is the covariance array.

 

  The diag(crossvar) is defined as:

 

         crossvar.diag = matrix( rep( NA, p^2), nrow = p)

         for ( i in 1: p )

           {

             for( j in 1: p )

              {

                crossvar.diag[ i, j ] = 0.5 * t ( x[ , i] ) % * % Q[ , , j ] % * % x[ , i ]  

              }

          }

 

Paul Lasky

P & B Consultants

Rancho Santa Fe, CA .