binnednp (version 0.4.0)

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

Value

A list with components

h_boot

Bootstrap bandwidth selector.

h_plugin

Plug-in bandwidth selector.

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.

References

TesisMiguel2015binnednp

JNS2016binnednp

Test2017binnednp

Examples

# NOT RUN {
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)

# }