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#main author: Kévin Allan Sales Rodrigues
#### uma medida de influencia
#' F Distance
#'
#' @param X A matrix or vector with explanatory variables.
#' @param y A vector with response variables.
#' @return
#' \item{F Distance}{ A vector with F Distance for each observation.}.
#'
#' @references Sun, R.-B. and Wei, B.-C. (2004) On influence assessment for lad regression.
#' \emph{Statistics & Probability Letters}, \strong{67}, 97-110. \doi{10.1016/j.spl.2003.08.018}.
#'
#'
#' @examples
#' ### Using stackloss data
#'
#' CookDistance(stack.loss, stack.x)
FD = function(y,X){
n = length(y)
###Calculando taoi que e o tao sem a i-esima observacao
###e calculando os betai que sao betai[,i]
beta = coef(ladfit(as.matrix(X), y))
betai = coef(ladfit(as.matrix(X)[-1,], y[-1]))
taoi = sum(abs(y-cbind(1,X)%*%as.matrix(betai)[,1]))
for (i in 2:n){
betai = cbind(betai, coef(ladfit(as.matrix(X)[-i,], y[-i])))
taoi = c(taoi, sum(abs(y-cbind(1,X)%*%as.matrix(betai)[,i])))
}
taoi = taoi/(n-1)
###Calculando LD(betai, taoi)
##por enquanto
#tao = 1.5088
tao = sum(abs(y-cbind(1,X)%*%as.matrix(coef(ladfit(X, y)))[,1]))/n
FF = tao^(-2)*sqrt(sum((cbind(1,X)%*%beta -cbind(1,X)%*%betai[,1])^(2)))
for (i in 2:n){
FF = c(FF, tao^(-2)*sqrt(sum((cbind(1,X)%*%beta -cbind(1,X)%*%betai[,i])^(2))))
}
plot(FF, main="F Distance", xlab="Indices",ylab="F Distance")
return(FF)
}
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