kdde function

Kernel density derivative estimate

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)

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

Returns

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

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.

s^(x)=−1{D2f^(x)<0}abs(∣D2f^(x)∣)hat(s)(x)=−1(D2hat(f)(x)<0)∗abs(det(D2hat(f)(x))) \hat{s}(\bold{x})= - \bold{1}\{\mathsf{D}^2 \hat{f}(\bold{x}) <0\} \mathrm{abs}(|\mathsf{D}^2 \hat{f}(\bold{x})|)hat(s)(x) = -1(D^2hat(f)(x) <0)*abs(det(D^2 hat(f)(x)))

where D2hat(f)(x)D^2 hat(f)(x) is the kernel Hessian matrix estimate. So hatshat{s} calculates the absolute value of the determinant of the Hessian matrix and whose sign is the opposite of the negative definiteness indicator.

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 packageRead PDF manual