ParLin_expectreg_homo_uni {locpolExpectile}

Partially linear expectile regression with a homoscedastic error and a univariate variable in the nonparametric function

Description

Formula interface for the partially linear expectile regression using local linear expectile estimation assuming a homoscedastic error and a univariate variable in the nonparametric function. For the nonparametric part, the general Rule-of-Thumb bandwidth selector proposed in Adam and Gijbels (2021a) is used. See Adam and Gijbels (2021b) for more details.

Usage

ParLin_expectreg_homo_uni(
  X,
  Y,
  Z,
  omega = 0.3,
  kernel = gaussK,
  grid = seq(min(Z), max(Z), length.out = 100)
)

Arguments

X

The covariates data values for the linear part (of size n \times k).

Y

The response data values.

Z

The covariate data values for the nonparametric part.

omega

Numeric vector of level between 0 and 1 where 0.5 corresponds to the mean.

kernel

The kernel used to perform the estimation. In default setting, kernel=gaussK. See details in Kernels.

grid

Vector of evaluation points used for the nonparametric part. In default setting, a grid of 100 equispaced grid-values on the domain of the variable Z.

Value

ParLin_expectreg_homo_uni partially linear expectile estimators for a homoscedastic error and a univariare variable in the nonparametric part proposed and studied by Adam and Gijbels (2021b). ParLin_expectreg_homo_uni returns a list whose components are:

• Linear The delta estimators for the linear part

• Nonlinear The estimation of the nonparametric part according to the grid.

References

Adam, C. and Gijbels, I. (2021a). Local polynomial expectile regression. Annals of the Institute of Statistical Mathematics doi:10.1007/s10463-021-00799-y.

Adam, C. and Gijbels, I. (2021b). Partially linear expectile regression using local polynomial fitting. In Advances in Contemporary Statistics and Econometrics: Festschrift in Honor of Christine Thomas-Agnan, Chapter 8, pages 139–160. Springer, New York.

Examples

library(locpol)
set.seed(123)
Z<-runif(100,-3,3)
eta_1<-rnorm(100,0,1)
X1<-(0.9*Z)+(1.5*eta_1)
set.seed(1234)
eta_2<-rnorm(100,0,2)
X2<-(0.9*Z)+(1.5*eta_2)
X<-rbind(X1,X2)

set.seed(12345)
epsilon<-rnorm(100,0,1)
delta<-rbind(0.8,-0.8)

Y<-as.numeric((t(delta)%*%X)+(10*sin(0.9*Z))+5*epsilon)

ParLin_expectreg_homo_uni(X=t(X),Y=Y,Z=Z,omega=0.3
,kernel=gaussK,grid=seq(min(Z),max(Z),length.out=10))