bpkde: Back-Projected Kernel Density Estimation

In bpkde: Back-Projected Kernel Density Estimation

Description

Compute a d-dimensional kernel density estimate using a back-projected kernel.

Usage

bpkde(data, alphas, kernel = dnorm, bw = bw.SJ, score.fun = M1, r = 7, padding = 4)

Arguments

data	a matrix or data frame. The data is coerced to a numeric matrix using the data.matrix function.
alphas	a numeric matrix of dimension d by K whose columns contain the directions (as unit vectors) used for the back projection. If missing, 90 equally space directions spanning the interval [-π/2, π/2) are used when d == 2 and 450 randomly chosen directions are used when d == 3. This argument must be provided for d >= 4.
kernel	a function for evaluating the univariate kernel.
bw	the function used to compute the univariate bandwidth estimates.
score.fun	the function used to compute the least squares cross-validation score for the kernel; see M0 and M1.
r	the computations are performed using linear binning and the discrete Fourier transform. The number of the grid points used is 2^r.
padding	a postive numeric value specifying the amount of zero-padding in units of bandwidth.

Value

a list with class c("bpkde", "mvkde") containing the following elements.

axes	a numeric matrix whose columns contain the grid points used along each axis to bin the data.
z	a numeric array containing the discrete kernel density estimate.
params	a list containing the optimal common scaling parameter omega.hat, the input set of directions alphas, and the computed univariate bandwidths lambdas.

References

Panaretos, Victor M. and Konis, Kjell (2012). Nonparametric Construction of Multivariate Kernels. Journal of the American Statistical Association 107(499):1085-1095.

Author(s)

Kjell Konis [e-mail]

Examples

data(Trimodal2)
f.hat <- bpkde(Trimodal2)

bpkde documentation built on May 2, 2019, 10:25 a.m.