kdcde function

Deconvolution kernel density derivative estimate

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

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

Returns

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)