Kernel feature significance
Kernel feature significance for 1- to 6-dimensional data.
kfs(x, H, h, deriv.order=2, gridsize, gridtype, xmin, xmax, supp=3.7,
eval.points, binned, bgridsize, positive=FALSE, adj.positive, w,
verbose=FALSE, signif.level=0.05)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 1-d data are positive. Default is FALSE. |
adj.positive |
adjustment applied to positive 1-d data |
w |
vector of weights. Default is a vector of all ones. |
verbose |
flag to print out progress information. Default is FALSE. |
signif.level |
overall level of significance for hypothesis tests. Default is 0.05. |
Feature significance is based on significance testing of the gradient (first derivative) and curvature (second derivative) of a kernel density estimate. Only the latter is currently implemented, and is also known as significant modal regions.
The hypothesis test at a grid point x is
H0(x): H f(x) < 0,
i.e. the density Hessian matrix H f(x) is negative definite.
The p-values are computed for each x using that
the test statistic is
approximately chi-squared distributed with d(d+1)/2 d.f.
We then use a Hochberg-type simultaneous testing procedure, based on the
ordered p-values, to control the
overall level of significance to be signif.level. If
H0(x) is rejected then x
belongs to a significant modal region.
The computations are based on kdde(x, deriv.order=2) so
kfs inherits its behaviour from kdde.
If the bandwidth H is missing from kfs, then
the default bandwidth is the plug-in selector
Hpi(,deriv.order=2). Likewise for missing h.
The effective support, binning, grid size, grid range, positive
parameters are the same as kde.
This function is similar to the featureSignif function in the
feature package, except that it accepts unconstrained bandwidth
matrices.
A kernel feature significance estimate is an object of class
kfs 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 |
binary matrix for significant feature 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. |
This is the same structure as a kdde object, except that
estimate is a binary matrix rather than real-valued.
Chaudhuri, P. & Marron, J.S. (1999) SiZer for exploration of structures in curves. Journal of the American Statistical Association, 94, 807-823.
Duong, T., Cowling, A., Koch, I. & Wand, M.P. (2008) Feature significance for multivariate kernel density estimation. Computational Statistics and Data Analysis, 52, 4225-4242.
Godtliebsen, F., Marron, J.S. & Chaudhuri, P. (2002) Significance in scale space for bivariate density estimation. Journal of Computational and Graphical Statistics, 11, 1-22.
library(MASS) data(geyser) geyser.fs <- kfs(geyser$duration, binned=TRUE) plot(geyser.fs, xlab="duration") ## see example in ? plot.kfs
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.