deepReg2d: Simple deepest regression method.

In DepthProc: Statistical Depth Functions for Multivariate Analysis

Description

This function calculates deepest regression estimator for simple regression.

Usage

deepReg2d(x, y)

Arguments

x	Independent variable.
y	Dependent variable.

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")

DepthProc documentation built on May 2, 2019, 6:22 p.m.