moderegbw: Cross-Validation Bandwidth Selector for Nonparametric Mode...

In lpme: Nonparametric Estimation of Measurement Error Models

Cross-Validation Bandwidth Selector for Nonparametric Mode Regression

Description

This function selects the bandwidth (Zhou and Huang, 2019) for the local polynomial estimators for nonparametric modal regression in the absence of measurement error.

Usage

moderegbw(Y, X, method="CV-density", p.order=0, h1=NULL, h2=NULL, nstart = 4,
          xinterval = quantile(X, probs=c(0.025, 0.975), names = FALSE),
          df=5, ncomp=5, nboot=5)

Arguments

Y	an n by 1 response vector.
X	an n by 1 predictor vector.
method	method="CV-density" is for density-based CV; method="CV-mode" is for mode-based CV; metohd="bootstrap" is for a bootstap method; see Zhou and Huang (2019) for details. For non-measurement error models, method="CV-mode" 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.
h1	bandwidth vector for h1; default is NULL, and h1 is chosen automatically. See Zhou and Huang (2019) 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 (2019) for details. It is recommended to carefully specify a fine grid for h2.
nstart	the starting number of modes for each grid value.
xinterval	the interval within which the modes will be estimated.
df	the degrees of freedom of splines used in the mixture normal regression for bootstrap method.
ncomp	the number of components used in the mixture normal regression for bootstrap method.
nboot	the number of bootstrap samples.

Value

The results include the bandwidth bw.

Author(s)

Haiming Zhou and Xianzheng Huang

References

Zhou, H. and Huang, X. (2019). Bandwidth selection for nonparametric modal regression. Communications in Statistics - Simulation and Computation, 48(4): 968-984.

See Also

moderegbwSIMEX,modereg

Examples

library(lpme)
## 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);
  }
}

## mode estimates
h1ref = c(1.06*sd(X)*n^(-0.2));
h2ref = c(1.06*sd(Y)*n^(-0.2));
## In practice moer fine grids are desired. 
hx = seq(h1ref*0.2, h1ref*1.5, length.out = 10); 
hy = seq(h2ref*0.8, h2ref, length.out = 2); 
hhxy = moderegbw(Y, X, method="CV-mode", p.order=0,
                 h1=hx, h2=hy)$bw;
fit = modereg(Y, X, xgrid=xgrid, bw=hhxy, 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.