aux-functions

 #################
 ### function mode
 #################
 require(modeest)
 mode <- function(x) {
         mode = mlv(x, method = "lientz", bw = 0.2)$M
         
 return(mode)
 }
 
 ##################################
 ### Trace of product of matrices
 ##################################
 tr <- function(A, B) {
       S = 0
       for (i in 1:dim(A)[1]) S = S + A[i,] %*% B[,i]
 return(as.numeric(S))
 }
 
 #############################################
 ### functions for bias and mean squared error
 #############################################
 biasMSE = function(x, par, li, ls) {
           x = x[x > li & x < ls]
 
           bias = par - mean(x)
           mse  = sum(par - x)^2/length(x)

           S = matrix(, 1, 3)
           colnames(S) = c('bias', 'mse', 'N')
           S[ ,1] = bias
           S[ ,2] = mse
           S[ ,3] = length(x)
 return(S)
 }