Kernel density derivative estimate
Kernel density derivative estimate for 1- to 6-dimensional data.
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)x |
matrix of data values |
H,h |
bandwidth matrix/scalar bandwidth. If these are missing, |
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 |
object |
object of class |
... |
other parameters |
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)(x) = -1(D^2 hat(f)(x) <0)*abs(det(D^2 hat(f)(x)))
where D^2 hat(f)(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.
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 |
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 |
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
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