R/cvbw.R

In Conake: Continuous Associated Kernel Estimation

cvbw <-
function(Vec,bw=NULL,ker,a=0,b=1){
###########################################################################################################
# INPUTS:
#   "Vec" 	:The sample of data 
#   "seq_bws"   :The sequence of bandwidths where 
#		     the CV function will be evaluated (and minimized)
#   "ker" 	: The kernel:  "dirDU" DiracDU,"bino" Binomial,"triang" Discrete Triangular.
#   "a" 	:The arm of the Dicrete Triangular kernel. Default value is 1.
#   "c" 	:The  number of categories in the dirDU kernel. Default value is 2.     
#    
# OUTPUT:Returns a list containing:
#   "hcv" 	: The bandwidth obtained by cross-validation
#   "CV"        : The cross validation values 
#   "seq_bws"	: The sequence of the bandwiths used
###########################################################################################################

if(is.null(bw)) {
	
		bw=seq((max(Vec)-min(Vec))/200,(max(Vec)-min(Vec))/2, length.out=100)
	    }


        result1<-0
	result2<-0
	x=seq(min(Vec),max(Vec),length.out=100)
	n1 <- length(x)
	n2 <- length(Vec)
	m1=matrix(0,n1,length(Vec))
	m2=matrix(0,n2,n2)
        Kef<-Vectorize(kef,vectorize.args=c('x','t')) 
      for(k in 1:length(bw)){
              m1 <-outer(x,Vec,Kef,bw[k],ker)
	      m2 <-outer(Vec,Vec,Kef,bw[k],ker) 
		
              res1<-apply(m1,1,mean)
	      diag(m2)<-0
	      res2<-apply(m2,1,sum)
              result1[k]=simp_int(x,res1^2)
	      result2[k]=(2/((n2-1)*n2))*sum(res2)
    }
  	CV=result1-result2    
	index<-which.min(CV)  #to compute the optimal bandwidth
	hcv<-bw[index]

	 return(list(hcv=hcv,CV=CV,bw=bw))

}