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kdcde

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 are obtained from from a quadratic programming problem, and then input into kde(,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.

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

Kernel Smoothing

v1.12.0

GPL-2 | GPL-3

Authors

Tarn Duong [aut, cre], Matt Wand [ctb], Jose Chacon [ctb], Artur Gramacki [ctb]

Initial release

2021-02-06