dpill Select a Bandwidth for Local Linear Regression

Description

Use direct plug-in methodology to select the bandwidth of a local linear Gaussian kernel regression estimate, as described by Ruppert, Sheather and Wand (1995).

Usage

dpill(x, y, blockmax = 5, divisor = 20, trim = 0.01, proptrun = 0.05, 
      gridsize = 401L, range.x, truncate = TRUE)

Arguments

x	numeric vector of x data. Missing values are not accepted.
y	numeric vector of y data. This must be same length as x, and missing values are not accepted.
blockmax	the maximum number of blocks of the data for construction of an initial parametric estimate.
divisor	the value that the sample size is divided by to determine a lower limit on the number of blocks of the data for construction of an initial parametric estimate.
trim	the proportion of the sample trimmed from each end in the x direction before application of the plug-in methodology.
proptrun	the proportion of the range of x at each end truncated in the functional estimates.
gridsize	number of equally-spaced grid points over which the function is to be estimated.
range.x	vector containing the minimum and maximum values of x at which to compute the estimate. For density estimation the default is the minimum and maximum data values with 5% of the range added to each end. For regression estimation the default is the minimum and maximum data values.
truncate	logical flag: if TRUE, data with x values outside the range specified by range.x are ignored.

Details

The direct plug-in approach, where unknown functionals that appear in expressions for the asymptotically optimal bandwidths are replaced by kernel estimates, is used. The kernel is the standard normal density. Least squares quartic fits over blocks of data are used to obtain an initial estimate. Mallow's Cp is used to select the number of blocks.

Value

the selected bandwidth.

Warning

If there are severe irregularities (i.e. outliers, sparse regions) in the x values then the local polynomial smooths required for the bandwidth selection algorithm may become degenerate and the function will crash. Outliers in the y direction may lead to deterioration of the quality of the selected bandwidth.

References

Ruppert, D., Sheather, S. J. and Wand, M. P. (1995). An effective bandwidth selector for local least squares regression. Journal of the American Statistical Association, 90, 1257–1270.

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

See Also

ksmooth, locpoly.

Examples

data(geyser, package = "MASS")
x <- geyser$duration
y <- geyser$waiting
plot(x, y)
h <- dpill(x, y)
fit <- locpoly(x, y, bandwidth = h)
lines(fit)