bda (version 3.2.0-3)

wkde: Compute a Binned Kernel Density Estimate for Weighted Data

Description

Returns x and y coordinates of the binned kernel density estimate of the probability density of the weighted data.

Usage

wkde(x, weights, freq, bw, from, to, gridsize, digits=0,
     rounding)

Arguments

x

A sample. 'NA' values will be automatically removed.

weights

A vector of weights of x

freq

A vector of frequencies of x

from,to,gridsize

start point, end point and size of a fine grid where the EDF will be evaluated.

digits

integer indicating the number of decimal places that x will be rounded to. Negative values are allowed. A negative number of digits means rounding to a power of ten, so for example digits = -2 rounds to the nearest hund

rounding

Rounding method. Options include nearest, up, down, or none.

bw

Smoothing parameter. Numeric or character value is allowed. If missing, mise -- LSCV bandwidth selector will be used.

Value

• a list containing the following components:
• x
  vector of sorted x values at which the estimate was computed.
• y
  vector of density estimates at the corresponding x.
• bw
  optimal bandwidth. sensitivity parameter, none NA if adaptive bandwidth selector is used.

encoding

UTF-8

Details

The default bandwidth, "nrd0", is computed using a rule-of-thumb for choosing the bandwidth of a Gaussian kernel density estimator based on weighted data. It defaults to 0.9 times the minimum of the standard deviation and the interquartile range divided by 1.34 times the sample size to the negative one-fifth power (= Silverman's ‘rule of thumb’, Silverman (1986, page 48, eqn (3.31)) _unless_ the quartiles coincide when a positive result will be guaranteed.

"nrd" is the more common variation given by Scott (1992), using factor 1.06.

"mise" is a completely automatic optimal bandwidth selector using the least-squares cross-validation (LSCV) method by minimizing the integrated squared errors (ISE). Implemented as in Wang and Wang (2007).

"amise" is a completely automatic adaptive optimal bandwidth selector using the least-squares cross-validation (LSCV) method by minimizing the integrated squared errors (ISE). Implemented as in Wang and Wang (2007).

"lscv" is a completely automatic optimal bandwidth selector using the least-squares cross-validation (LSCV) method by minimizing the integrated squared errors (ISE). Implemented using the Fast Fourier Transformation.

erd is a rule-of-thumb bandwidth selector using an exponential reference. Good for survival data.

aMAE is a automatic bandwidth selector designed for survival data subject to random right-censoring. It selects the bandwidth locally by minimizing a mean absolute error (Kuhn and Padgett (1997)).

If bandwidth is missing, the MISE bandwidth selector will be used by default.

References

Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.

Wang, B. and Wang, X-F. (2007). "Bandwidth Selection for Weighted Kernel Density Estimation".

Kuhn, J.P. and Padgett, W.J. (1997). "Local bandwidth selection for kernel density estimation from right-censored data based on asymptotic mean absolute error". Nonlinear Analysis, Theory, Methods & Applications. 30, 4375-4384.

Examples

mu = 34.5; s=2.5; n = 1000
 x = round(rnorm(n, mu, s),1)
 x0 = seq(min(x)-s,max(x)+s, length=100)
 f0 = dnorm(x0,mu, s);  ymax <- max(f0*1.2)

 xt = table(x); n = length(x)
 x1 = as.numeric(names(xt))
 w1 = as.numeric(xt)
 
 est1 <- wkde(x1,freq=w1, bw='nrd0')
 est2 <- wkde(x1,freq=w1, bw='nrd')
 est3 <- wkde(x1,freq=w1, bw='amise')
 est4 <- wkde(x1,freq=w1, bw='mise')
 est6 <- wkde(x1,freq=w1, bw='erd')
 est7 <- wkde(x1,freq=w1, bw='lscv')

 est0 = density(x1,bw="SJ",weights=w1/sum(w1)); 

 plot(f0~x0, xlim=c(min(x),max(x)), ylim=c(0,ymax), 
   xlab="x", ylab="Density", type="l")
 lines(est0, col=1, lty=2, lwd=2)

 lines(est1, col=2)
 lines(est2, col=3)
 lines(est3, col=4)
 lines(est4, col=5)
 lines(est6, col=4,lty=2)
 lines(est7, col=6)

 legend(max(x),ymax,xjust=1,yjust=1,cex=.8,
  legend=c("N(34.5,1.5)", "SJ", "nrd0",
  "nrd","amise","mise","erd","lscv"),
  col = c(1,1,2,3,4,5,4,6), 
  lty = c(1,2,1,1,1,1,2,1),
  lwd=c(1,2,1,1,1,1,1,1))