bw.dens.binned: Bootstrap and plug-in bandwidth selectors for kernel density...

In binnednp: Nonparametric Estimation for Interval-Grouped Data

Description

Bootstrap and plug-in bandwidth selectors for kernel density estimation with binned data.

Usage

bw.dens.binned(n, y, w, ni, gboot, pilot.type = 3, hn = 100,
  plugin.type = "N", confband = FALSE, alpha = 0.05, B = 1000,
  plot = TRUE, print = TRUE, model, parallel = FALSE,
  pars = new.env())

Arguments

n	Positive integer. Size of the complete sample.
y	Vector. Observed values. They define the extremes of the sequence of intervals in which data is binned.
w	Vector. Proportion of observations within each interval.
ni	Vector. Number of observations within each interval.
gboot	Positive real number. Pilot bandwidth for the bootstrap bandwidth selector.
pilot.type	1, 2 or 3. If gboot is missing, pilot bandwidth for the bootstrap bandwidth selector is automatically selected using methods 1, 2 or 3. Defaults to 3. See details for more information.
hn	Positive integer. Size of the grid of bandwidths for which MISE will be approximated. Defaults to 100.
plugin.type	Character. If plugin.type = "N", normality is assumed at the last step when calculating the plug-in bandwidth. If plugin.type = "A", parameter at last step is estimated nonparametrically using gplugin as bandwidth. Otherwise, the unknown parameter is estimated fitting a normal mixture. Defaults to type = "N".
confband	Logical. If TRUE, bootstrap confidence bands are constructed for the density function. Defaults to FALSE.
alpha	Real number between 0 and 1. Significance level for the bootstrap confidence bands. Defaults to 0.05.
B	Positive integer. Number of bootstrap resamples used when constructing confidence bands. Defaults to 1000.
plot	Logical. If TRUE, kernel density estimators are plotted along with (optional) bootstrap confidence bands. Defaults to TRUE.
print	Logical. If TRUE and confband is TRUE, the percentage of bootstrap resamples already evaluated is printed. Defaults to TRUE.
model	Character. Name of the parametric family of distributions to be fitted for the grouped sample. Parameters are estimated by maximum likelihood.
parallel	Logical. If TRUE, confidence bands are estimated using parallel computing with sockets.
pars	Environment. Needed for the well functioning of the script. DO NOT modify this argument.

Details

If pilot.type = 1, an heuristic rule is used for calculating the pilot bandwidth. It's not recommended when population's density function is suspected to be highly multimodal.

If pilot.type = 2, the pilot bandwidth is such that the kernel density estimator with bandwidth gboot approximates the histogram of the grouped sample minimizing the residual sum of squares. If pilot.type = 3, a penalty is imposed on the curvature of the kernel density estimator with bandwidth gboot. The penalty parameter is selected as to best approximate the curvature of the true density.

Value

A list with components

h_boot	Bootstrap bandwidth selector.
h_plugin	Plug-in bandwidth selector.

References

\insertRef

TesisMiguel2015binnednp

\insertRef

JNS2016binnednp

\insertRef

Test2017binnednp

Examples

set.seed(1)
n <- 200 #complete sample size
k <- 30 #number of intervals
x <- rnorm(n,6,1) #complete sample
y <- seq(min(x)-0.2,max(x)+0.2,len=k+1) #intervals
w <- c(sapply(2:k,function(i)sum( x<y[i]&x>=y[i-1] )), sum(x<=y[k+1]&x>=y[k]) )/n #proportions
bw.dens.binned(n,y,w,plot=FALSE)

binnednp documentation built on June 8, 2019, 1:02 a.m.