Simple deepest regression method.

deepReg2d(x, y)

Arguments

Details

Function originates from an original algorithm proposed by Rousseeuw and Hubert. Let Zn=(x1,y1),...,(xn,yn)⊂Rd denotes a sample considered from a following semiparametric model: yl=a0+a1x1l+...+a(d−1)lx(d−1)l+εl,l=1,...,n, we calculate a depth of a fit α=(a0,...,ad−1) as RD(α,Zn)=u≠0min♯l:rl(α)uTxl<0,l=1,...,n, where r(⋅) denotes the regression residual, α=(a0,...,ad−1), uTxl≠0. The deepest regression estimator DR(α,Zn) is defined as DR(α,Zn)=α≠0argmaxRD(α,Zn)

References

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

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), 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"
)