Qest (version 1.0.1)

wtrunc: Weighting Function for Qest, Qlm, and Qcoxph.

Description

This function can be used within a call to Qest, Qlm, or Qcoxph to assign a different weight to each quantile.

Usage

wtrunc(tau, delta.left = 0.05, delta.right = 0.05, smooth = FALSE, sigma = 0.01)

Value

A vector of weights assigned to each quantile.

Arguments

tau

a vector of quantiles.

delta.left, delta.right

proportion of quantiles to be removed from the left and righ tail. The weighting function is 1 in the interval (delta.left, 1 - delta.right), and zero elsewhere. Default is delta.left = 0.05 and delta.right = 0.05. When a weighting function is used to counteract the effect of extreme observations, delta.left is a guess for the proportion of outliers on the left tail; and delta.right is a guess for the proportion of outliers on the right tail.

smooth

if smooth = TRUE the indicator functions used to construct wtrunc(tau) are replaced by integrated Gaussian kernels. Default smooth = FALSE.

sigma

the bandwith of a Gaussian kernel. This parameter controls the smoothness of the weighting function, and is ignored if smooth = FALSE. Default sigma = 0.01.

Author

Gianluca Sottile <[e-mail]>, Paolo Frumento <[e-mail]>

Details

Within a call to Qest, Qlm, or Qcoxph, one may want to assign a different weight to each quantile through the optional argument wtau. This can be done for reasons of efficiency, or to counteract the presence of outliers. While wtau can be any user-defined function, one can use wtrunc as a shortcut to construct a weighting function that truncates a certain subset of quantiles in the tails of the distribution. For instance, the estimator defined by Qest(..., wtau = wtrunc, delta.left = 0.05, delta.right = 0.1) only uses quantiles in the interval (0.05, 0.90) to fit the model. In this example, delta.left = 0.05 is a guess for the proportion of outliers on the left tail; and delta.right is a guess for the proportion of outliers on the right tail. Use smooth = TRUE to replace the indicator functions involved in wtrunc with smooth functions. Introducing a weighting function that only assigns a positive weight to the quantiles that correspond to the ``healthy'' part of the distribution allows to deal with any level of contamination by outliers.

See Also

Qest, Qlm, Qcoxph.

Examples

if (FALSE) {
taus <- seq(0, 1, length.out = 1000)

### zero weight to quantiles above 0.95
plot(taus, wtrunc(taus, delta.left = 0, delta.right = 0.05),
  type = "l", lwd = 1.5)
# smooth counterpart
lines(taus, wtrunc(taus, delta.left = 0, delta.right = 0.05,
  smooth = TRUE, sigma = .01), col = 2, lwd = 1.5)
lines(taus, wtrunc(taus, delta.left = 0, delta.right = 0.05,
  smooth = TRUE, sigma = .05), col = 3, lwd = 1.5)

### zero weight to quantiles below 0.05
plot(taus, wtrunc(taus, delta.left = 0.05, delta.right = 0),
  type = "l", lwd = 1.5)
# smooth counterpart
lines(taus, wtrunc(taus, delta.left = 0.05, delta.right = 0,
  smooth = TRUE, sigma = .01), col = 2, lwd = 1.5)
lines(taus, wtrunc(taus, delta.left = 0.05, delta.right = 0,
  smooth = TRUE, sigma = .05), col = 3, lwd = 1.5)


### zero weight to quantiles below 0.05 and above 0.90
plot(taus, wtrunc(taus, delta.left = 0.05, delta.right = 0.10),
  type = "l", lwd = 1.5)
# smooth counterpart
lines(taus, wtrunc(taus, delta.left = 0.05, delta.right = 0.10,
  smooth = TRUE, sigma = .01), col = 2, lwd = 1.5)
lines(taus, wtrunc(taus, delta.left = 0.05, delta.right = 0.10,
  smooth = TRUE, sigma = .05), col = 3, lwd = 1.5)


### Use wtrunc in Qest, Qlm, Qcoxph
# Qest(..., wtau = wtrunc, delta.left = 0.05, delta.right = 0.1)
}