dpilc {sharpPen}

Select a Bandwidth for Local Quadratic and Cubic Regression

Description

Use direct plug-in methodology to select the bandwidth of a local quadratic and local cubic Gaussian kernel regression estimate, as an extension of Wand's dpill function.

Usage

dpilc(xx, yy, blockmax = 5, divisor = 20, trim = 0.01,
                 proptrun = 0.05, gridsize = 401L, range.x = range(x))

Arguments

xx

numeric vector of x data. Missing values are not accepted.

yy

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.

Details

This function is a local cubic (also quadratic) extension of the dpill function of Wand's KernSmooth package. The kernel is the standard normal density. Least squares octic fits over blocks of data are used to obtain an initial estimate. As in Wand's implementation of the Ruppert, Sheather and Wand selector, Mallow's C_p is used to select the number of blocks. An option is available to make use of a periodic penalty (with possible trend) relating the 4th derivative of the regression function to a constant (gamma) times the 2nd derivative. This avoids the need to calculate the octic fits and reverts back to the original quartic fits of dpill with appropriate adjustments to the estimated functionals needed in the direct-plug-in bandwidth calculation. This code is similar to dpilq but uses a 6th degree polyomial approximation instead of an 8th degree polynomial approximation.

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.

Author(s)

D.Wang and W.J.Braun

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

x <- faithful$eruptions
y <- faithful$waiting
plot(x, y)
h <- dpill(x, y)
fit <- locpoly(x, y, bandwidth = h, degree=1)
lines(fit)
h <- dpilc(x, y)
fit <- locpoly(x, y, bandwidth = h, degree=2)
lines(fit, col=3, lwd=2)
fit <- locpoly(x, y, bandwidth = h, degree=3)
lines(fit, col=2, lwd=2)