h_GenROT_bivariate {locpolExpectile}

Rule-of-Thumb bandwidth selectors for bivariate covariate setting

Description

General Rule-of-Thumb bandwidth selector for the expectile regression proposed by Adam and Gijbels (2021b) see Formula (26) for a bivariate covariate setting. The weight functions are chosen to be equal to the indicator functions on [min(Z_{ki})+0.1,max(Z_{ki})-0.1] for k=1,2 (i.e. for the two covariates) and j=0 and p=1.

Usage

h_GenROT_bivariate(Z1, Z2, Y, omega, kernel = gaussK)

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.

Value

h_GenROT_bivariate provides the general Rule-of-Thumb bandwidth selector for the expectile regression, in the bivariate covariate setting, proposed by Adam and Gijbels (2021b).

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)

h=h_GenROT_bivariate(Z1=Z_1,Z2=Z_2,Y=Y,kernel=gaussK,omega=0.1)
#h=0.1241427