expectreg_loclin_bivariate {locpolExpectile}

Local linear expectile regression (iterative procedure) for a bivariate covariate case

Description

Formula interface for the local linear expectile estimation for a bivariate covariate case.

Usage

expectreg_loclin_bivariate(
  Z1,
  Z2,
  Y,
  omega,
  kernel = gaussK,
  h,
  grid = cbind(seq(min(Z1), max(Z1), length.out = length(Z1)), seq(min(Z2), max(Z2),
    length.out = length(Z2)))
)

Arguments

Z1

The first covariate data values.

Z2

The second covariate data values.

Y

The response data values.

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.

h

Smoothing parameter, bandwidth.

grid

Matrix of evaluation points. In default setting, a grid of equispaced grid-values on the domain of the variables Z1 and Z2.

Value

expectreg_loclin_bivariate local linear expectile estimator proposed and studied by Adam and Gijbels (2021b) for a bivariate covariate case. expectreg_loclin_bivariate returns a matrix whose components are the estimation of the bivariate expectile surface, of order \omega according to the grid matrix. The rows are the grid on the first covariate data values (i.e. Z1) and the columns the grid on the second covariate data values (i.e. Z2).

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 139–160. Springer, New York.

Examples

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)

expectreg_loclin_bivariate(Z1=Z_1,Z2=Z_2,Y=Y,omega=0.1
,kernel=gaussK,h=0.1,grid=cbind(seq(min(Z_1),max(Z_1)
,length.out=10),seq(min(Z_2),max(Z_2),length.out=10)))