kdde: Kernel density derivative estimate

In ks: Kernel Smoothing

Kernel density derivative estimate

Description

Kernel density derivative estimate for 1- to 6-dimensional data.

Usage

kdde(x, H, h, deriv.order=0, gridsize, gridtype, xmin, xmax, supp=3.7, 
    eval.points, binned, bgridsize, positive=FALSE, adj.positive, w,
    deriv.vec=TRUE, verbose=FALSE)
kcurv(fhat, compute.cont=TRUE)

## S3 method for class 'kdde'
predict(object, ..., x)

Arguments

x	matrix of data values
H, h	bandwidth matrix/scalar bandwidth. If these are missing, Hpi or hpi is called by default.
deriv.order	derivative order (scalar)
gridsize	vector of number of grid points
gridtype	not yet implemented
xmin, xmax	vector of minimum/maximum values for grid
supp	effective support for standard normal
eval.points	vector or matrix of points at which estimate is evaluated
binned	flag for binned estimation
bgridsize	vector of binning grid sizes
positive	flag if data are positive (1-d, 2-d). Default is FALSE.
adj.positive	adjustment applied to positive 1-d data
w	vector of weights. Default is a vector of all ones.
deriv.vec	flag to compute all derivatives in vectorised derivative. Default is TRUE. If FALSE then only the unique derivatives are computed.
verbose	flag to print out progress information. Default is FALSE.
compute.cont	flag for computing 1% to 99% probability contour levels. Default is TRUE.
fhat	object of class kdde with deriv.order=2
object	object of class kdde
...	other parameters

Details

For each partial derivative, for grid estimation, the estimate is a list whose elements correspond to the partial derivative indices in the rows of deriv.ind. For points estimation, the estimate is a matrix whose columns correspond to the rows of deriv.ind.

If the bandwidth H is missing from kdde, 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.

The summary curvature is computed by kcurv, i.e.

\hat{s}(\bold{x})= - \bold{1}\{\mathsf{D}^2 \hat{f}(\bold{x}) < 0\} \mathrm{abs}(|\mathsf{D}^2 \hat{f}(\bold{x})|)

where \mathsf{D}^2 \hat{f}(\bold{x}) is the kernel Hessian matrix estimate. So \hat{s} calculates the absolute value of the determinant of the Hessian matrix and whose sign is the opposite of the negative definiteness indicator.

Value

A kernel density derivative estimate is an object of class kdde 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 derivative 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
deriv.order	derivative order (scalar)
deriv.ind	martix where each row is a vector of partial derivative indices

See Also

kde

Examples

set.seed(8192)
x <- rmvnorm.mixt(1000, mus=c(0,0), Sigmas=invvech(c(1,0.8,1)))
fhat <- kdde(x=x, deriv.order=1) ## gradient [df/dx, df/dy]
predict(fhat, x=x[1:5,])

## See other examples in ? plot.kdde

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