ParLin_expectreg_hetero: Partially linear expectile regression with different possible...

In locpolExpectile: Local Polynomial Expectile Regression

Description

Formula interface for the partially linear expectile regression using local linear expectile estimation for different heteroscedastic error structure and a univariate variable in the nonparametric function g(.). The model is of the form Y=δ^T X + g(Z) + σ(X) ε, Y=δ^T X + g(Z) + σ(Z) ε or Y=δ^T X + g(Z) + σ(Z,X) ε. See Table 1 in Adam and Gijbels (2021b) for more details.

Usage

ParLin_expectreg_hetero(
  X,
  Y,
  Z,
  omega = 0.3,
  kernel = gaussK,
  heteroscedastic = c("X", "Z", "Z and X")
)

Arguments

X	The covariates data values for the linear part (of size n \times k with k=1 or k=2).
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.
heteroscedastic	Heteroscedastic error depending on X, or onZ or on Z and X

Value

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

• If the heteroscedastic error depends on Z:

  • Linear The delta estimators for the linear part

  • Nonlinear The estimation of the nonparametric part according to the observed values Z_i.

• If the heteroscedastic error depends on X:

  • Linear The delta estimators for the linear part

  • Nonlinear_g The estimation of the nonparametric part according to the observed values Z_i.

  • Nonlinear_g_omega The estimation of the nonparametric part according to the observed values X_i (if X is univariate) or to the couple of observed values (X_{1i},X_{2j}).

• If the heteroscedastic error depends on Z and X:

  • Linear The delta estimators for the linear part

  • Nonlinear_g The estimation of the nonparametric part according to the couple of the observed values (Z_i,X_j) (if X is univariate) or to the observed values (Z_i,X_{1i},X_{2i}).

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)
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))+(0.6*X1^2)*epsilon)

ParLin_expectreg_hetero(X=t(X),Y=Y,Z=Z,omega=0.3,kernel=gaussK,heteroscedastic="X")

locpolExpectile documentation built on Aug. 3, 2021, 5:07 p.m.