featureSignif: Feature significance for kernel density estimation
In feature: Local Inferential Feature Significance for Multivariate Kernel Density Estimation

Description Usage Arguments Details Value References See Also Examples

View source: R/featureSignif.R

Identify significant features of kernel density estimates of 1- to 4-dimensional data.

1 2	featureSignif(x, bw, gridsize, scaleData=FALSE, addSignifGrad=TRUE, addSignifCurv=TRUE, signifLevel=0.05)

`x`	data matrix
`bw`	vector of bandwidth(s)
`gridsize`	vector of estimation grid sizes
`scaleData`	flag for scaling the data i.e. transforming to unit variance for each dimension.
`addSignifGrad`	flag for computing significant gradient regions
`addSignifCurv`	flag for computing significant curvature regions
`signifLevel`	significance level

Feature significance is based on significance testing of the gradient (first derivative) and curvature (second derivative) of a kernel density estimate. This was developed for 1-d data by Chaudhuri & Marron (1995), for 2-d data by Godtliebsen, Marron & Chaudhuri (1999), and for 3-d and 4-d data by Duong, Cowling, Koch & Wand (2007).

The test statistic for gradient testing is at a point x is

W(x) = || hat{grad f}(x; H)||^2

where hat{grad f}(x; H) is kernel estimate of the gradient of f(x) with bandwidth H, and ||.|| is the Euclidean norm. W(x) is approximately chi-squared distributed with d degrees of freedom where d is the dimension of the data.

The analogous test statistic for the curvature is

W2(x) = ||vech hat{curv f}(x; H)||^2

where hat{curv f}(x; H) is the kernel estimate of the curvature of f(x), and vech is the vector-half operator. W2(x) is approximately chi-squared distributed with d(d+1)/2 degrees of freedom.

Since this is a situation with many dependent hypothesis tests, we use the Hochberg multiple comparison testing procedure to control the overall level of significance. See Hochberg (1988) and Duong, Cowling, Koch & Wand (2007).

Returns an object of class fs which is a list with the following fields

`x`	data matrix
`names`	name labels used for plotting
`bw`	vector of bandwidths
`fhat`	kernel density estimate on a grid
`grad`	logical grid for significant gradient
`curv`	logical grid for significant curvature
`gradData`	logical vector for significant gradient data points
`gradDataPoints`	significant gradient data points
`curvData`	logical vector for significant curvature data points
`curvDataPoints`	significant curvature data points

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.

Hochberg, Y. (1988) A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75, 800-802.

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.

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

featureSignifGUI, plot.fs

## Univariate example
data(earthquake)
eq3 <- -log10(-earthquake[,3])
fs <- featureSignif(eq3, bw=0.1)
plot(fs, addSignifGradRegion=TRUE)

## Bivariate example
library(MASS)
data(geyser)
fs <- featureSignif(geyser)
plot(fs, addKDE=FALSE, addData=TRUE)  ## data only
plot(fs, addKDE=TRUE)                 ## KDE plot only
plot(fs, addSignifGradRegion=TRUE)    
plot(fs, addKDE=FALSE, addSignifCurvRegion=TRUE)
plot(fs, addSignifCurvData=TRUE, curvCol="cyan")

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found 
4: no DISPLAY variable so Tk is not available