Introduction
Kernel smoothing for data from 1- to 6-dimensions. This package forms the basis for the practical data analysis in the book Multivariate Kernel Smoothing and Its Applications.
There are three main types of functions in this package:
- computing kernel estimators - these function names begin with
k - computing bandwidth selectors - these begin with
h(1-d) orH(>1-d) - displaying kernel estimators - these begin with
plot.
The kernel used throughout is the normal (Gaussian) kernel. For 1-d data, the bandwidth h is the standard deviation of the normal kernel, whereas for multivariate data, the bandwidth matrix H is the variance matrix.
The main function kde() computes a kernel density estimate. For display, its plot method calls plot.kde(). The bandwidth choice is crucial for the performance of kernel estimators. There are several varieties of bandwidth selectors available
- plug-in
hpi(1-d);Hpi,Hpi.diag(2- to 6-d) - least squares (or unbiased) cross validation (LSCV or UCV)
hlscv(1-d);Hlscv,Hlscv.diag(2- to 6-d) - biased cross validation (BCV)
Hbcv,Hbcv.diag(2- to 6-d) - smoothed cross validation (SCV)
hscv(1-d);Hscv,Hscv.diag(2- to 6-d) - normal scale
hns(1-d);Hns(2- to 6-d).
For an example with bivariate data, see vignette("ks").
The other types of kernel estimators follow a similar functionality.
Further reading
Chacon, J.E. & Duong, T. (2018) Multivariate Kernel Smoothing and Its Applications. Chapman & Hall/CRC Press, Boca Raton.
Duong, T. (2004) Bandwidth Matrices for Multivariate Kernel Density Estimation Ph.D. Thesis, University of Western Australia.