README.md

In ks: Kernel Smoothing

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 from CRAN:

install.packages("ks") 

Further reading

Chacon, J.E. & Duong, T. (2018) Multivariate Kernel Smoothing and Its Applications. Chapman & Hall/CRC, Boca Raton.

Duong, T. (2004) Bandwidth Matrices for Multivariate Kernel Density Estimation Ph.D. Thesis, University of Western Australia.

ks documentation built on May 9, 2026, 5:07 p.m.