ks (version 1.6.13)

kdde: Kernel density dereivative estimate for multivariate data

Description

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

Usage

kdde(x, H, h, deriv.order, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points, 
    binned=FALSE, bgridsize, positive=FALSE, adj.positive, w)

Arguments

x

matrix of data values

H

bandwidth matrix

h

scalar bandwidth

deriv.order

derivative order

gridsize

vector of number of grid points

gridtype

not yet implemented

xmin

vector of minimum values for grid

xmax

vector of maximum values for grid

supp

effective support for standard normal is [-supp, supp]

eval.points

points at which density estimate is evaluated

binned

flag for binned estimation (default is FALSE)

bgridsize

vector of binning grid sizes - required if binned=TRUE

positive

flag if 1-d data are positive (default is FALSE)

adj.positive

adjustment added to data i.e. when positive=TRUE KDE is carried out on log(x + adj.positive). Default is the minimum of x.

w

vector of weights (non-negative and sum is equal to sample size)

Value

• Kernel density estimate is an object of class kde which is a list with 4 fields
• x
  data points - same as input
• eval.points
  points at which the density estimate is evaluated
• estimate
  density estimate at eval.points.
• H
  bandwidth matrix
• h
  scalar bandwidth (1-d only)
• w
  weights
• deriv.order
  derivative order (scalar)
• deriv.ind
  each row is a vector of partial derivative indices of the vectorised derivative (contains duplicates)

Details

For d = 1, 2, 3, 4, and if eval.points is not specified, then the density derivative estimate is computed over a grid defined by gridsize (if binned=FALSE) or by bgridsize (if binned=TRUE).

For d = 1, 2, 3, 4, and if eval.points is specified, then the density derivative estimate is computed exactly at eval.points. For d > 4, the kernel density derivative estimate is computed exactly and eval.points must be specified.

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 rows of deriv.ind.

The default xmin is min(x) - Hmax*supp and xmax is max(x) + Hmax*supp where Hmax is the maximim of the diagonal elements of H.

The default weights w is a vector of all ones.

References

Wand, M.P. & Jones, M.C. (1995) Kernel Smoothing. Chapman & Hall. London.

See Also

kde

Examples

## univariate example
x <- rnorm.mixt(n=100, mus=1, sigmas=1, props=1)
fhat1 <- kdde(x=x, h=hpi(x), deriv.order=1)      ## df/dx 
fhat2 <- kdde(x=x, h=hpi(x), deriv.order=2)      ## d^2 f/dx^2 

## bivariate example
data(unicef)
H.scv <- Hscv(x=unicef)
fhat1 <- kdde(x=unicef, H=H.scv, deriv.order=1)   ## gradient vector
fhat2 <- kdde(x=unicef, H=H.scv, deriv.order=2)   ## vectorised Hessian matrix