Simple deepest regression method.

Description

This function calculates deepest regression estimator for simple regression.

Usage

deepReg2d(x, y)

Arguments

Details

Function originates from an original algorithm proposed by Rousseeuw and Hubert. Let {Z}^{n}={ (x_1,y_1),...,(x_n,y_n)} {subset {R}^{d} } denotes a sample considered from a following semiparametric model: {{y}_{l}}={{a}_{0}}+{{a}_{1}}{{x}_{1l}}+...+{{a}_{(d-1)l}}{{x}_{(d-1)l}}+{{varepsilon }_{l}}, l=1,...,n, we calculate a depth of a fit α=(a_{0},...,a_{d-1}) as RD(α ,{{Z}^{n}})={u\ne 0}{{min }},sharp{l: frac{{{r}_{l}}(α )}{{{u}^{T}}{{x}_{l}}}<0,l=1,...,n}, where r(cdot ) denotes the regression residual, α=(a_{0},...,a_{d-1}) , {u}^{T}{x}_{l}\ne 0 . The deepest regression estimator DR(α,{{Z}^{n}}) is defined as

DR(α ,{{Z}^{n}})={α \ne 0}{{arg max }},RD(α ,{{Z}^{n}})

Author(s)

Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.

References

Rousseeuw J.P., Hubert M. (1998), Regression Depth, Journal of The American Statistical Association, vol.94.

Examples

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")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DepthProc)
Loading required package: ggplot2
Loading required package: Rcpp
Loading required package: rrcov
Loading required package: robustbase
Scalable Robust Estimators with High Breakdown Point (version 1.3-11)

Loading required package: MASS
Loading required package: np
Nonparametric Kernel Methods for Mixed Datatypes (version 0.60-2)
[vignette("np_faq",package="np") provides answers to frequently asked questions]
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DepthProc/deepReg2d.Rd_%03d_medium.png", width=480, height=480)
> ### Name: deepReg2d
> ### Title: Simple deepest regression method.
> ### Aliases: deepReg2d
> 
> ### ** Examples
> 
> 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")
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>