Deconvolution kernel density derivative estimate

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

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

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.

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)