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) or H (>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.

Installation

Install the latest release version from CRAN:

install.packages("ks") 

Geospatial and tidy data analysis

The functionality in the ks package is ported to the sister eks package. The latter can substantially simplify workflows for geospatial and tidy data analysis.

If the input are geospatial data, then the output are also geospatial and are compatible with base R and ggplot2 graphics. Likewise, if the input are tidy data, then output are also tidy and are compatible with ggplot2 graphics.

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.