h_GenROT_without {locpolExpectile}

Rule-of-Thumb bandwidth selectors in a location-scale setting without using the one-to-one mapping

Description

Rule-of-Thumb bandwidth selector for the expectile regression in a location scale without using the one-to-one mapping. The weight function is chosen to be equal to the indicator function on [min(X_i)+0.1,max(X_i)-0.1].

Usage

h_GenROT_without(X, Y, j = 0, p = 1, kernel = gaussK, omega)

compDerEstError_exp(X, Y, p, omega)

Arguments

X

The covariate data values.

Y

The response data values.

j

The order of derivative to estimate. In default setting, j=0.

p

The order of the local polynomial estimator. In default setting, p=1.

kernel

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

omega

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

Value

h_GenROT_without provides the Rule-of-Thumb bandwidth selector in a location-scale setting without using the one-to-one mapping for univariate expectile regression proposed by Adam and Gijbels (2021a).

compDerEstError_exp returns a data frame whose components are:

• X The covariate data values.

• Y The response data values.

• fit The fitted values for the parametric estimation.

• der The derivative estimation at X values.

• err The estimation of the error vector

• err_fit The \omegath expectile of the residuals

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

h=h_GenROT_without(X=x,Y=y,j=0,p=1,kernel=gaussK,omega=0.3)
#h=1.937706