binnednp (version 0.4.0)

bw.dist.binned.boot: Bootstrap bandwidth selector for kernel distribution estimation and binned data.

Description

Bootstrap bandwidth selector for kernel distribution estimation and binned data.

Usage

bw.dist.binned.boot(n, y, w, ni, g, pilot.type = 2, nit = 10,
  confband = FALSE, B = 1000, alpha = 0.05, print = TRUE,
  plot = TRUE, 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.

g

Positive real number. Pilot bandwidth. If missing, plug-in N bandwidth for the distribution is considered.

pilot.type

1 or 2. If g is missing, pilot bandwidth for the bootstrap bandwidth selector is automatically selected using methods 1 or 2. Defaults to 1. See details for more information.

nit

Positive integer. Number of iterations in the dichotomy algorithm for the estimation of the bootstrap bandwidth.

confband

Logical. If TRUE, bootstrap confidence bands are constructed for the estimator. Defaults to FALSE.

B

Positive integer. Number of bootstrap resamples used for the construction of the confidence bands. Defaults to 1000.

alpha

Real number between 0 and 1. Significance level for the confidence bands. Defaults to 0.05

print

Logical. If TRUE, script current status is printed. Defaults to TRUE.

plot

Logical. If TRUE, results are plotted. Defaults to FALSE.

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

Bootstrap bandwidth for the distribution function.

Fh

Function. Kernel distribution estimator with bandwidth h.

confband (optional)

Matrix. Its columns contain the bootstrap confidence bands for the estimator.

Details

If pilot.type = 1, plug-in bandwidth for the distribution is considered as pilot bandwidth for the bootstrap selector.

If pilot.type = 2, the pilot bandwidth is such that the kernel distribution estimator with bandwidth g approximates the empirical distribution of the grouped sample minimizing the residual sum of squares. Also, a penalty is imposed on the global slope of the kernel density estimator with bandwidth g. The penalty parameter is selected as to best approximate the global slope of the true density.

References

TesisMiguel2015binnednp

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.dist.binned.boot(n,y,w,plot=FALSE)

# }