SCBmeanfd (version 1.1)

plugin.select: Plug-in Bandwidth Selection for Local Polynomial Estimation

Description

Select the plug-in bandwidth described in Benhenni and Degras (2011) for the local polynomial estimation of a mean function and its first derivative based on functional data.

Usage

plugin.select(x, y, drv = 0L, degree = drv + 1L)

Arguments

x

numeric vector of x data. This observation grid must be uniform and missing values are not accepted.

y

matrix or data frame with functional observations (= curves) stored in rows. The number of columns of y must match the length of x. Missing values are not accepted.

drv

order of the derivative to estimate. Must be 0 or 1.

degree

degree of local polynomial used. Must equal drv or drv+1.

Value

the plug-in bandwidth.

Details

The plug-in method should not be used with small data sets, since it is based on asymptotic considerations and requires reasonably accurate estimates of derivatives of the mean and covariance functions. Both the number of observed curves and observation points should be moderate to large. The plug-in bandwidth is designed to minimize the asymptotic mean integrated squared estimation error $$AMISE(h) = \int (\mu(x) - \hat{\mu}(x; h))^2 dx,$$ where $mu(x)$ is the mean function and $mu.hat(x;h)$ is a local polynomial estimator with kernel bandwidth $h$. The expression of the plug-in bandwidth can be found in Benhenni and Degras (2011).

References

Benhenni, K. and Degras, D. (2011). Local polynomial estimation of the average growth curve with functional data. http://arxiv.org/abs/1107.4058

See Also

cv.select

Examples

## Not run: 
# ## Phoneme data
# data(phoneme)
# classes <- phoneme[,151]
# phoneme <- phoneme[,-151]
# freq    <- 1:150
# plugin.bandwidth  <- numeric(5) 
# cv.bandwidth  <- numeric(5)  # compare with cross-validation
# for (i in 1:5) {
#   plugin.bandwidth[i] <- plugin.select(x = freq, y = phoneme[classes == i, ],
#                           drv = 0, degree = 1) 
#   cv.bandwidth[i]     <- cv.select(x = freq, y = phoneme[classes == i, ], 
#                           degree = 1)
# }
# 
# round(cbind(plugin.bandwidth, cv.bandwidth), 4)
# 
# ## End(Not run)