meanregbwSIMEX {lpme} | R Documentation |
This function selects the bandwidth for both the DFC (Delaigle, Fan, and Carroll, 2009) and HZ (Huang and Zhou, 2017) estimators.
meanregbwSIMEX(Y, W, method="HZ", sig, error="laplace", k_fold=5, B=10,
h1=NULL, h2=NULL, length.h=10, lconst=0.5, rconst=2, Wdiff=NULL)
Y |
an n by 1 response vector. |
W |
an n by 1 predictor vector. |
method |
the method to be used; |
sig |
standard deviation of the measurement error. |
error |
the distribution assumed for the measurement error; |
k_fold |
gives fold of cross-validation to be used; default is 2. |
B |
total number of cross-validation criteria to average over; defualt is 10. |
h1 |
bandwidth vector for the first level error contamination; default is |
h2 |
bandwidth vector for the second level error contamination; defualt is |
length.h |
number of grid points for each of h1 and h2; default is 10. |
lconst , rconst |
used to control the searching windows for bandwidths h1 and h2. For example, |
Wdiff |
an n by 1 vector of |
The results include the bandwidth bw
.
Haiming Zhou and Xianzheng Huang
Huang, X. and Zhou, H. (2017). An alternative local polynomial estimator for the error-in-variables problem. Journal of Nonparametric Statistics, 29: 301-325.
Delaigle, A. and Hall, P. (2008). Using SIMEX for smoothing-parameter choice in errors-in-variables problems. Journal of the American Statistical Association, 103: 280-287.
#############################################
## X - True covariates
## W - Observed covariates
## Y - individual response
library(lpme)
## generate laplace
rlap=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 gofx(x) to estimate
gofx = function(x){ 2*x*exp(-10*x^4/81) }
## Generate data
sigma_e = 0.2;
sigma_x = 1; X = rnorm(n, 0, sigma_x);
## Sample Y
Y = gofx(X) + rnorm(n, 0, sigma_e);
## reliability ratio
lambda=0.85;
sigma_u = sqrt(1/lambda-1)*sigma_x;
print( sigma_x^2/(sigma_x^2 + sigma_u^2) );
#W=X+rnorm(n,0,sigma_u);
W=X+rlap(n,0,sigma_u/sqrt(2));
#### SIMEX
#**Note: larger values for B and length.h are needed for accurate estimates.
#**e.g., k_fold=5, B=10, length.h=10 will be generally good.
hwNEW = meanregbwSIMEX(Y, W, method="HZ", sig=sigma_u, error="laplace", k_fold=2,
B=1, length.h=1)$bw
ghat_NEW = meanreg(Y, W, hwNEW , method="HZ", sig=sigma_u, error="laplace");
## plots
x = ghat_NEW$xgrid;
plot(x, gofx(x), "l", main="Individual", lwd="2")
lines(ghat_NEW$xgrid, ghat_NEW$yhat, lty="dashed", col="2",lwd="3")