PowT.1tau.func {EXRQ}

Estimation for Quantile Power Transformation Model

Description

This function estimates the power transformation parameter at a single given quantile level

Usage

PowT.1tau.func(y, x, tau, lams = seq(-2, 2, 0.1), a)

Arguments

y

a vector of length n representing the response

x

a n x p matrix of n observations and p predictors

tau

the quantile level of interest

lams

a set of transformation parameters for grid search

a

the location shift

Details

This function estimates the transformation parameter lam following the estimation method in Mu and He (2007) such that the conditional quantile of the transformed response is linear in covariates. The transformed response is defined as

\Lambda(y) = {(y+a)^\lambda-1}\lambda, if \lambda \neq 0; =log(y+a) if \lambda=0.

Value

A list is returned with the following components

lam: the estimated transformation parameter

coef: the estimated quantile coefficient from the power-transformed linear quantile regression

References

Mu, Y. and He, X. (2007). Power transformation toward a linear regression quantile. Journal of the American Statistical Association, 102, 269-279.