kdcde: Deconvolution kernel density derivative estimate

In ks: Kernel Smoothing

Deconvolution kernel density derivative estimate

Description

Deconvolution kernel density derivative estimate for 1- to 6-dimensional data.

Usage

kdcde(x, H, h, Sigma, sigma, reg, bgridsize, gridsize, binned, 
      verbose=FALSE, ...)
dckde(...) 

Arguments

x	matrix of data values
H, h	bandwidth matrix/scalar bandwidth. If these are missing, Hpi or hpi is called by default.
Sigma, sigma	error variance matrix
reg	regularisation parameter
gridsize	vector of number of grid points
binned	flag for binned estimation
bgridsize	vector of binning grid sizes
verbose	flag to print out progress information. Default is FALSE.
...	other parameters to kde

Details

A weighted kernel density estimate is utilised to perform the deconvolution. The weights w are the solution to a quadratic programming problem, and then input into kde(,w=w). This weighted estimate also requires an estimate of the error variance matrix from repeated observations, and of the regularisation parameter. If the latter is missing, it is calculated internally using a 5-fold cross validation method. See Hazelton & Turlach (2009). dckde is an alias for kdcde.

If the bandwidth H is missing from kde, then the default bandwidth is the plug-in selector Hpi. Likewise for missing h.

The effective support, binning, grid size, grid range, positive parameters are the same as kde.

Value

A deconvolution kernel density derivative estimate is an object of class kde which is a list with fields:

x	data points - same as input
eval.points	vector or list of points at which the estimate is evaluated
estimate	density estimate at eval.points
h	scalar bandwidth (1-d only)
H	bandwidth matrix
gridtype	"linear"
gridded	flag for estimation on a grid
binned	flag for binned estimation
names	variable names
w	vector of weights
cont	vector of probability contour levels

References

Hazelton, M. L. & Turlach, B. A. (2009), Nonparametric density deconvolution by weighted kernel density estimators, Statistics and Computing, 19, 217-228.

See Also

kde

Examples

data(air)
air <- air[, c("date", "time", "co2", "pm10")]
air2 <- reshape(air, idvar="date", timevar="time", direction="wide")
air <- as.matrix(na.omit(air2[,c("co2.20:00", "pm10.20:00")]))
Sigma.air <- diag(c(var(air2[,"co2.19:00"] - air2["co2.21:00"], na.rm=TRUE),
   var(air2[,"pm10.19:00"] - air2[,"pm10.21:00"], na.rm=TRUE)))
fhat.air.dec <- kdcde(x=air, Sigma=Sigma.air, reg=0.00021, verbose=TRUE)
plot(fhat.air.dec, drawlabels=FALSE, display="filled.contour", lwd=1)

ks documentation built on Sept. 30, 2024, 9:15 a.m.