moderegbwSIMEX: Cross-Validation Bandwidth Selector Using SIMEX for...

In lpme: Nonparametric Estimation of Measurement Error Models

Cross-Validation Bandwidth Selector Using SIMEX for Nonparametric Mode Regression

Description

This function selects the bandwidth (Zhou and Huang, 2016) for the local polynomial estimators for nonparametric modal regression in the presence of measurement error.

Usage

moderegbwSIMEX(Y, W, method="CV-density", p.order=0, sig, B=5, 
               h1=NULL, h2=NULL, length.h=10, CIregion=0.95, nstart=4)

Arguments

Y	an n by 1 response vector.
W	an n by 1 predictor vector.
method	method="CV-density" is for density-based CV; method="CV-mode" is for mode-based CV; see Zhou and Huang (2016) for details. For measurement error models, method="CV-density" is recommended.
p.order	the order of polynomial, up to 1; p.order=0 returns local constant estimators and p.order=1 returns local linear estimators.
sig	standard deviation of the measurement error.
B	total number of cross-validation criteria to average over; defualt is 5.
h1	bandwidth vector for h1; default is NULL, and h1 is chosen automatically. See Zhou and Huang (2016) for details. It is recommended to carefully specify a fine grid for h1.
h2	bandwidth vector for h2; default is NULL, and h2 is chosen automatically. See Zhou and Huang (2016) for details. It is recommended to carefully specify a fine grid for h2.
length.h	number of grid points for each of h1 and h2; default is 10.
CIregion	used to determine the interval on which the mode is estimated.
nstart	the starting number of modes for each grid value.

Value

The results include the bandwidth bw.

Author(s)

Haiming Zhou and Xianzheng Huang

References

Zhou. H. and Huang, X. (2016). Nonparametric modal regression in the presence of measurement error. Electronic Journal of Statistics, 10: 3579-3620.

See Also

modereg, moderegbw

Examples

library(lpme)

rlaplace=function (use.n, location = 0, scale = 1) 
{
  location <- rep(location, length.out = use.n)
  scale <- rep(scale, length.out = use.n)
  rrrr <- runif(use.n)
  location - sign(rrrr - 0.5) * scale * 
    (log(2) + ifelse(rrrr < 0.5, log(rrrr), log1p(-rrrr)))
}

## sample size:
n =100;
## Function m(x) to estimate#
gofx1  = function(x){ (x+x^2) }
gofx2  = function(x){ (x+x^2)-6 }
xgrid	= seq(-2, 2, length.out=100); 
ngrid	= length(xgrid)

## Sample X
X = rnorm(n, 0, 1); sigma_x=1;
## Sample Y
Y = rep(0, n);
U = runif(n);
for(i in 1:n){
  if(U[i]<0.5){
    Y[i] = rnorm(1, gofx1(X[i]), 1);
  }else{
    Y[i] = rnorm(1, gofx2(X[i]), 1);
  }
}
## reliability ratio
lambda=0.9;
sigma_u  = sqrt(1/lambda-1)*sigma_x;
W=X+rlaplace(n,0,sigma_u/sqrt(2));

## mode estimates
hhxy = c(0.15, 1)
## Note you needs to use the following code to calculate bandwidth
## It is not run here due to the time constrain of runing examples. 
#hhxy = moderegbwSIMEX(Y, W, method="CV-density", p.order=0, 
#                      sig=sigma_u, B=5, length.h=10)$bw;
fit = modereg(Y, W, xgrid=xgrid, bw=hhxy, sig=sigma_u, p.order=0,
              PLOT=TRUE);

## Plot
plot(xgrid, gofx1(xgrid), "l", lwd="2", ylim=c(-9,7), xlim=c(-2,2));
lines(xgrid, gofx2(xgrid), "l", lwd="2");
points(rep(fit$xgrid,fit$x.num), fit$mode, col="3",lwd="2")

lpme documentation built on May 10, 2022, 1:05 a.m.