llqr {BwQuant}

Fitting a local linear quantile regression model

Description

Function that estimates the quantile regression function using a local linear kernel smoother.

Usage

llqr(x, y, tau, t, h)

Arguments

x

numeric vector of x data.

y

numeric vector of y data. This must be the same length as x.

tau

the quantile order where the regression function is to be estimated. It must be a number strictly between 0 and 1.

t

the values of x at which the quantile regression model is to be estimated.

h

the bandwidth parameter.

Value

A list with the following components:

x.values

the given points at which the evaluation occurs.

y.values

the estimated values of the quantile regression function at the given x.values.

Author(s)

Mercedes Conde-Amboage and Cesar Sanchez-Sellero.

References

Fan, J., Hu, T. C. and Truong, Y. K. (1994). Robust nonparametric function estimation. Scandinavian Journal of Statistics, 21, 433-446.

Yu, K. and Jones, M. C. (1998). Local linear quantile regression. Journal of the American Statistical Association, 93, 228-237.

See Also

The argument h with the bandwidth parameter can be fixed to some arbitrary value or chosen by one of the procedures implemented in the functions bwCV, bwPI, bwRT or bwYJ.

Examples

set.seed(1234)
x=runif(100)
y=10*(x^4+x^2-x)+rexp(100)
tau=0.25
h=bwPI(x,y,tau)
t=seq(0,1,length=101)
m=llqr(x,y,tau,t,h)
plot(x,y)
lines(m$x.values,m$y.values)