meanregbwSIMEX: Cross-Validation Bandwidth Selector Using SIMEX for Nonparametric Mean Regression

Description

This function selects the bandwidth for both the DFC (Delaigle, Fan, and Carroll, 2009) and HZ (Huang and Zhou, 2017) estimators.

Usage

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)

Arguments

an n by 1 response vector.

an n by 1 predictor vector.

method

the method to be used; method="HZ" uses the estimator proposed by Huang and Zhou (2017); method="DFC" uses the estimator proposed by Delaigle, Fan, and Carroll (2009). It currently does not support bandwidth selection for naive estimators.

sig

standard deviation of the measurement error.

error

the distribution assumed for the measurement error; error="laplace" is for Laplace distribution; error="normal" is for Gaussian distribution. It currently does not support user-assumed distribution.

k_fold

gives fold of cross-validation to be used; default is 2.

total number of cross-validation criteria to average over; defualt is 10.

bandwidth vector for the first level error contamination; default is NULL, and h1 is chosen automatically. See Huang and Zhou (2017) for details.

bandwidth vector for the second level error contamination; defualt is NULL, and h2 is chosen automatically. See Huang and Zhou (2017) for details.

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, seq(bw1*lconst,bw1*rconst,length.out=length.h) is used to obtain bandwidth grid points for h1, where bw1 is an initial bandwidth; see Huang and Zhou (2017) for details of finding the initial bandwith.

Wdiff

an n by 1 vector of (W1-W2)/2, where W1, W2 are two replicated measurements; default is NULL, which indicates that the errors are generated from the assumed error distribution, otherwise, the errors are generated from Wdiff with replacement.

Value

The results include the bandwidth bw.

References

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.

Examples

Run this code

# NOT RUN {
#############################################
## 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")
# }