locpoly: Estimate Functions Using Local Polynomials

In KernSmooth: Functions for Kernel Smoothing Supporting Wand & Jones (1995)

Estimate Functions Using Local Polynomials

Description

Estimates a probability density function, regression function or their derivatives using local polynomials. A fast binned implementation over an equally-spaced grid is used.

Usage

locpoly(x, y, drv = 0L, degree, kernel = "normal", 
        bandwidth, gridsize = 401L, bwdisc = 25, 
        range.x, binned = FALSE, truncate = TRUE)

Arguments

x	numeric vector of x data. Missing values are not accepted.
bandwidth	the kernel bandwidth smoothing parameter. It may be a single number or an array having length gridsize, representing a bandwidth that varies according to the location of estimation.
y	vector of y data. This must be same length as x, and missing values are not accepted.
drv	order of derivative to be estimated.
degree	degree of local polynomial used. Its value must be greater than or equal to the value of drv. The default value is of degree is drv + 1.
kernel	"normal" - the Gaussian density function. Currently ignored.
gridsize	number of equally-spaced grid points over which the function is to be estimated.
bwdisc	number of logarithmically-equally-spaced bandwidths on which bandwidth is discretised, to speed up computation.
range.x	vector containing the minimum and maximum values of x at which to compute the estimate.
binned	logical flag: if TRUE, then x and y are taken to be grid counts rather than raw data.
truncate	logical flag: if TRUE, data with x values outside the range specified by range.x are ignored.

Value

if y is specified, a local polynomial regression estimate of E[Y|X] (or its derivative) is computed. If y is missing, a local polynomial estimate of the density of x (or its derivative) is computed.

a list containing the following components:

x	vector of sorted x values at which the estimate was computed.
y	vector of smoothed estimates for either the density or the regression at the corresponding x.

Details

Local polynomial fitting with a kernel weight is used to estimate either a density, regression function or their derivatives. In the case of density estimation, the data are binned and the local fitting procedure is applied to the bin counts. In either case, binned approximations over an equally-spaced grid is used for fast computation. The bandwidth may be either scalar or a vector of length gridsize.

References

Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.

See Also

bkde, density, dpill, ksmooth, loess, smooth, supsmu.

Examples

data(geyser, package = "MASS")
# local linear density estimate
x <- geyser$duration
est <- locpoly(x, bandwidth = 0.25)
plot(est, type = "l")

# local linear regression estimate
y <- geyser$waiting
plot(x, y)
fit <- locpoly(x, y, bandwidth = 0.25)
lines(fit)

KernSmooth documentation built on May 29, 2024, 11 a.m.