bda (version 1.2.7-31)

bootkde: To compute a bootstrap kernel density estimate

Description

To compute a bootstrap kernel density estimate based on data that are rounded.

Usage

bootkde(x, method='z.score',scale=1, rounding = 'nearest',
                    from, to, alpha=0.05, gridsize=512L,na.rm=TRUE, iter=100)
## S3 method for class 'bcb':
plot(x, main = NULL, xlab = "x", ylab = "Probability",
            lwd=1, col=1, lty=1, zero.line = TRUE,
            bgcol='gray',scb=FALSE, ...)
## S3 method for class 'bcb':
lines(x, lwd=1, col=1, lty=1, bgcol='gray', scb=FALSE, ...)
## S3 method for class 'bcb':
print(x, digits = NULL, ...)

Arguments

x

Raw data (a vector).

method

Method to compute the confidence bands. Default: 'z.score'. Other options include 'quantile'.

scale

The scale that the data are rounded. Default: 1.

rounding

Method to round the data: up/down, or to the nearest integers.

from,to

range of x where the densities are evaluated .

alpha

Significance level to compute the confidence bands.

na.rm

Remove missing values by default.

iter

Iteration number used to construct the bootstrap confidence bands. Default: 100.

gridsize

The size of grid where the densities will be evaluated.

scb

An indicator to specify whether or not to draw the pointwise confidence bands.

bgcol

Define the color of the confidence bands.

main,xlab,ylab,lwd,col,lty,zero.line,digits,...

Controls

Value

• y
  Densities
• x
  Grid points where the densities are evaluated
• ucb,lcb
  The upper and lower confidence bands over 'x'.

Details

If 'method=z.score', the confidence bands are computed by first computing the standard error of point estimate at x based on B bootstrap samples, then compute the margin of error by using z-score.

If 'method=quantile', the 100*(alpha/2) and 100*(1-alpha/2) quantiles are found at x.

If data are rounded to the nearest integers, 'scale=1'. In some other cases, for example if the birth weights are rounded to the '100g', 'scale=100'.

References

Wang, B. and Wertelecki, W. (2012) Density Estimation for Data With Rounding Errors. Computational Statistics and Data Analysis, (in press), doi: 10.1016/j.csda.2012.02.016.

See Also

rounding

Examples

#(b = (mean(x)^2)/(var(x)+mean(x)^2))
#k = seq(0.00001,10,length=10000)
#gk = exp(lgamma(1+1/k)*2) - b*exp(lgamma(1+2/k))
#plot(gk~k,type='l')
#abline(h=0, col=2,lwd=.1)
#sele = !is.na(gk)
#gk2 = abs(gk[sele])
#k2 = k[sele]
#alpha = k[which(gk2==min(gk2))]
#lambda = mean(x)/gamma(1+1/alpha)
#c(alpha,lambda)

data(birth)
(ofc = rounding(birth$Head))
(bwt = rounding(birth$Weight, scale=100))
(out0 = bfmm(ofc, m=1))

mu = 34.5; s = 1.5
y = rnorm(100,mu,s) #raw data
x = round(y) #rounded data
binx = rounding(x)

x0 = seq(min(y)-sd(y),max(y)+sd(y),length=200)
f0 = dnorm(x0,mu,s)

##  Fit a single well-known distribution to binned data

xmin=29; xmax = 41;
hist(binx,xlim=c(29,41))
lines(f0~x0, col = 1)
lines(density(x+runif(length(x))-.5), col=1,lty=2)

out1 = bfmm(x, m=1, type='normal')
lines(density(out1), col=2)

out2 = bfmm(x, m=1, type='gamma')
lines(density(out2), col=4)

out3 = bfmm(x, m=1, type='weibull')
lines(density(out3), col=3)

out4 = bfmm(x, m=1, type='beta')
lines(density(out4), col=5)

out5 = bfmm(x,m=2)
lines(density(out5), col=2,lwd=3)

legend(xmax, max(binx$counts)/sum(binx$counts),
  xjust=1,yjust=1,
  legend=c("true","kde(x+u)","normal","gamma","weibull","beta","normal m=2"),
  col = c(1,1,2,4,3,5,2), lty=c(1,2,1,1,1,1,1),lwd=c(1,1,1,1,1,1,3))

##  Fit with different methods

hist(binx,xlim=c(29,41))
lines(f0~x0, col = 1)
lines(density(x+runif(length(x))-.5), col=1,lty=2)

out6 = bfmm(x, m=2, method='nelder')
lines(density(out6), col=2,lwd=1)

out7 = bfmm(x, m=2, method='newton')
lines(density(out7), col=3,lwd=1)

out8 = bfmm(x, m=1, method='nelder')
lines(density(out8), col=4,lwd=1)

out9 = bfmm(x, m=1, method='newton')
lines(density(out9), col=5,lwd=1)

out10 = bfmm(x, mu=c(34,36), method='newton')
lines(density(out10), col=6,lwd=1)