expectreg_locpol {locpolExpectile}

Local polynomial expectile regression (iterative procedure), univariate covariate

Description

Formula interface for the local polynomial expectile estimation.

Usage

expectreg_locpol(
  X,
  Y,
  j = 0,
  p = 1,
  omega,
  h,
  kernel = gaussK,
  starting_value = c("mean", "median", "omega-quantile"),
  grid = seq(min(X), max(X), length.out = 100)
)

Arguments

X

The covariate data values.

Y

The response data values.

j

The order of derivative of the expectile to be estimated. In default setting, j=0 (i.e. estimating the expectile regression function).

p

The order of the local polynomial estimator. In default setting, p=1 (i.e. local linear estimator).

omega

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

h

Smoothing parameter, bandwidth.

kernel

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

starting_value

Method for the starting point. Choice between the estimated (unconditional) mean, median and omega-quantile.

grid

Vector of evaluation points. In default setting, a grid of 100 equispaced grid-values on the domain of the variable X.

Value

expectreg_locpol local polynomial expectile estimator proposed and studied by Adam and Gijbels (2021a).

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.

Examples

library(locpol)
data(mcycle)
y=mcycle$accel
x=mcycle$times

expectreg_locpol(X=x,Y=y,omega=0.3,h=0.4,kernel=gaussK,starting_value="mean"
,grid=seq(min(x),max(x),length.out=10))