Rearrangement.estimation {LorenzRegression}

Estimates a monotonic regression curve via Chernozhukov et al (2009)

Description

Rearrangement.estimation estimates the increasing link function of a single index model via the methodology proposed in Chernozhukov et al (2009).

Usage

Rearrangement.estimation(Y, Index, t = Index, weights = NULL, degree.pol = 1)

Arguments

Y

The response variable.

Index

The estimated index. The user may obtain it using function Lorenz.Reg.

t

A vector of points over which the link function H(.) should be estimated. Default is the estimated index.

weights

vector of sample weights. By default, each observation is given the same weight.

degree.pol

degree of the polynomial used in the local polynomial regression. Default value is 1.

Details

A first estimator of the link function, neglecting the assumption of monotonicity, is obtained with function locpol from the locpol package. The final estimator is obtained through the rearrangement operation explained in Chernozhukov et al (2009). This operation is carried out with function rearrangement from package Rearrangement.

Value

A list with the following components

t

the points over which the estimation has been undertaken.

H

the estimated link function evaluated at t.

References

Chernozhukov, V., I. Fernández-Val, and A. Galichon (2009). Improving Point and Interval Estimators of Monotone Functions by Rearrangement. Biometrika 96 (3). 559–75.

See Also

Lorenz.Reg, locpol, rearrangement

Examples

data(Data.Incomes)
PLR <- Lorenz.Reg(Income ~ ., data = Data.Incomes, penalty = "SCAD",
                  h.grid = nrow(Data.Incomes)^(-1/5.5), eps = 0.01)
Y <- PLR$Fit[,1]
Index <- PLR$Fit[,2]
Rearrangement.estimation(Y = Y, Index = Index)