R/deepreg2d.R

In depthproc: depthproc

#'@title Simple deepest regression method.
#'@export
#'  @description This function calculates deepest regression estimator for simple regression.
#'
#'  @param x Independent variable.
#'  @param y Dependent variable.
#'
#'  @details 
#' Function originates from an original algorithm proposed by Rousseeuw and Hubert. Let  \eqn{ {Z}^{n}={ (x_1,y_1),...,(x_n,y_n)} {\subset {R}^{d} }}  denotes a sample considered from a following semiparametric model:  \eqn{ {{y}_{l}}={{a}_{0}}+{{a}_{1}}{{x}_{1l}}+...+{{a}_{(d-1)l}}{{x}_{(d-1)l}}+{{\varepsilon }_{l}}},  \eqn{l=1,...,n}, we calculate a depth of a fit  \eqn{ \alpha=(a_{0},...,a_{d-1}) }  as  \eqn{ RD(\alpha ,{{Z}^{n}})={u\ne 0}{{\min }}\,\sharp{l: \frac{{{r}_{l}}(\alpha )}{{{u}^{T}}{{x}_{l}}}<0,l=1,...,n}}, where  \eqn{ r(\cdot ) }  denotes the regression residual,  \eqn{ \alpha=(a_{0},...,a_{d-1}) } ,  \eqn{ {u}^{T}{x}_{l}\ne 0 } .  {The deepest regression estimator}  \eqn{ DR(\alpha,{{Z}^{n}}) }  is defined as 
#' 
#' \eqn{ DR(\alpha ,{{Z}^{n}})={\alpha \ne 0}{{\arg \max }}\,RD(\alpha ,{{Z}^{n}})}
#'
#'
#'  @references
#'  Rousseeuw J.P., Hubert M. (1998), Regression Depth, \emph{Journal of The American Statistical Association},  vol.94.
#'  
#'  @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'  
#'  @examples
#'  
#EXAMPLE 1
#'  data(pension)
#'  plot(pension)
#'  abline(lm(Reserves~Income,data = pension), lty = 3, lwd = 2) #lm
#'  abline(deepReg2d(pension[,1],pension[,2]), lwd = 2) #deepreg2d
#'  #EXAMPLE 2
#'  data(under5.mort)
#'  data(inf.mort)
#'  data(maesles.imm)
#'  data2011=na.omit(cbind(under5.mort[,22],inf.mort[,22],maesles.imm[,22]))
#'  x<-data2011[,3]
#'  y<-data2011[,2]
#'  plot(x,y,cex=1.2, ylab="infant mortality rate per 1000 live birth", xlab="against masles immunized #'  percentage", main='Projection Depth Trimmed vs. LS regressions')
#'  abline(lm(x~y,data = pension), lwd = 2, col='black') #lm
#'  abline(deepReg2d (x,y), lwd = 2,col='red') #trimmed reg
#'  legend("bottomleft",c("LS","DeepReg"),fill=c("black","red"),cex=1.4,bty="n")
deepReg2d<-function(x,y)
{
  y <- y[order(x)]
  x <- sort(x)
  tmp = depth2dcpp(x,y)
  new("DeepReg2d", coef = tmp[2:1], depth = tmp[3])
}