QRIndiv {QRegVCM}

Individual quantile objective function

Description

The estimation of conditional quantile curves using individual quantile objective function.

Usage

QRIndiv(VecX, tau, times, subj, X, y, d, kn, degree, lambda, gam)

Arguments

VecX

The representative values for each covariate used to estimate the desired conditional quantile curves.

tau

The quantiles of interest.

times

The vector of the time variable.

subj

The vector of subjects/individuals.

X

The covariate matrix containing 1 as its first column (including intercept in the model).

y

The response vector.

d

The order of the differencing operator for each covariate.

kn

The number of knots for each covariate.

degree

The degree of the B-spline basis function for each covariate.

lambda

The grid for the smoothing parameter to control the trade of between fidelity and penalty term (use a fine grid of lambda).

gam

The power used in estimating the smooting parameter for each covariate (e.g. gam=1 or gam=0.5).

Value

alpha

The estimator of the coefficient vector of the basis B-splines.

hat_bt

The varying coefficients estimators.

qhat

The conditional quantile curves estimator.

Note

Some warning messages are related to the function rq.fit.sfn.

Author(s)

Yudhie Andriyana

References

Andriyana, Y., Gijbels, I., and Verhasselt, A. P-splines quantile regression estimation in varying coefficient models. Test 23, 1 (2014a),153–194.

See Also

rq.fit.sfn as.matrix.csr truncSP

Examples

data(PM10)

PM10 = PM10[order(PM10$day,PM10$hour,decreasing=FALSE),]

y = PM10$PM10[1:200]
times = PM10$hour[1:200]
subj = PM10$day[1:200]
dim = length(y)
x0 = rep(1,200)
x1 = PM10$cars[1:200]
x2 = PM10$wind.speed[1:200]

X = cbind(x0, x1, x2)

VecX = c(1, max(x1), max(x2))

##########################
#### Input parameters ####
##########################
kn = c(10, 10, 10)
degree = c(3, 3, 3)
taus = seq(0.1,0.9,0.1)
lambdas = c(1,1.5,2)
d = c(1, 1, 1)
gam = 1/2
##########################


qhat = QRIndiv(VecX=VecX, tau=taus, times=times, subj=subj, X=X,
		y=y, d=d, kn=kn, degree=degree, lambda=lambdas, gam=gam)$qhat

qhat1 = qhat[,1]
qhat2 = qhat[,2]
qhat3 = qhat[,3]
qhat4 = qhat[,4]
qhat5 = qhat[,5]
qhat6 = qhat[,6]
qhat7 = qhat[,7]
qhat8 = qhat[,8]
qhat9 = qhat[,9]


i = order(times, y, qhat1, qhat2, qhat3, qhat4, qhat5, qhat6, qhat7,
    qhat8, qhat9);

times = times[i]; y = y[i]; qhat1 = qhat1[i]; qhat2=qhat2[i];
qhat3=qhat3[i]; qhat4=qhat4[i]; qhat5=qhat5[i]; qhat6=qhat6[i];
qhat7=qhat7[i]; qhat8=qhat8[i]; qhat9=qhat9[i];

ylim = range(qhat1, qhat9)
plot(qhat1~times, col="magenta", cex=0.2, lty=5, lwd=2, type="l",
    ylim=ylim, xlab="hour", ylab="PM10");
lines(qhat2~times, col="aquamarine4", cex=0.2, lty=4, lwd=2);
lines(qhat3~times, col="blue", cex=0.2, lty=3, lwd=3);
lines(qhat4~times, col="brown", cex=0.2, lty=2, lwd=2);
lines(qhat5~times, col="black", cex=0.2, lty=1, lwd=2);
lines(qhat6~times, col="orange", cex=0.2, lty=2, lwd=2)
lines(qhat7~times, col="darkcyan", cex=0.2, lty=3, lwd=3);
lines(qhat8~times, col="green", cex=0.2, lty=4, lwd=2);
lines(qhat9~times, col="red", cex=0.2, lty=5, lwd=3)

legend("bottom", c(expression(tau==0.9), expression(tau==0.8),
      expression(tau==0.7), expression(tau==0.6), expression(tau==0.5),
      expression(tau==0.4), expression(tau==0.3), expression(tau==0.2),
      expression(tau==0.1)), ncol=1, col=c("red","green","darkcyan",
      "orange","black","brown","blue","aquamarine4","magenta"),
      lwd=c(2,2,3,2,2,2,3,2,2), lty=c(5,4,3,2,1,2,3,4,5))