locpolExpectile (version 0.1.1)

ParLin_expectreg_homo_biv: Partially linear expectile regression with a homoscedastic error and a bivariate variable in the nonparametric function

Description

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

Usage

ParLin_expectreg_homo_biv(
  X,
  Y,
  Z,
  omega = 0.3,
  kernel = gaussK,
  grid = cbind(seq(min(Z[, 1]), max(Z[, 1]), length.out = 10), seq(min(Z[, 2]), max(Z[,
    2]), length.out = 10))
)

Arguments

X

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

Y

The response data values.

Z

The covariates data values for the nonparametric part (of size \(n \times 2\)).

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

Matrix of evaluation points used for the nonparametric part. In default setting, a grid of 10 equispaced grid-values in each direction on the domain of the variable Z.

Value

ParLin_expectreg_homo_biv partially linear expectile estimators assuming a homoscedastic error and a bivariate covariate in the nonparametric part, proposed and studied by Adam and Gijbels (2021b). ParLin_expectreg_homo_biv 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. The rows of the estimation matrix are the grid on the first covariate data values (i.e. Z[,1]) and the columns the grid on the second covariate data values (i.e. Z[,2]).

References

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<U+2013>160. Springer, New York.

Examples

# NOT RUN {
library(locpol)
library(lestat)
set.seed(6)
dist <- muniformdistribution(rep(0, 2), rep(1, 2))
values<-simulate(dist,200)
Z_1<-values[,1]
Z_2<-values[,2]
Z<-rbind(Z_1,Z_2)
gamma=cbind(3,-0.4)
set.seed(7)
eta_1<-rnorm(100,0,1)
X1=(gamma%*%Z)+(1.5*eta_1)
set.seed(8)
eta_2<-rnorm(100,0,2)
X2=(gamma%*%Z)+(1.5*eta_2)
X<-rbind(X1,X2)
set.seed(9)
epsilon<-rt(100,3)
delta_true<-rbind(0,-0.8)
Y=as.numeric((t(delta_true)%*%X)+(0.2*exp(1.5*(gamma%*%Z)))+epsilon)

ParLin_expectreg_homo_biv(X=t(X),Y=Y,Z=t(Z),omega=0.1,kernel=gaussK
,grid=cbind(seq(min(Z[,1]),max(Z[,1]),length.out=10),seq(min(Z[,2]),max(Z[,2]),length.out=10)))


# }