bandwidth.CV: Choice of the bandwidth by cross validation.
In extremefit: Estimation of Extreme Conditional Quantiles and Probabilities

Description Usage Arguments Details Value Author(s) References See Also Examples

Choose a bandwidth by minimizing the cross validation function.

1
2
3

bandwidth.CV(X, t, Tgrid, hgrid, pcv = 0.99,
  kernel = TruncGauss.kernel, kpar = NULL, CritVal = 3.6,
  plot = FALSE)

`X`	a vector of the observed values.
`t`	a vector of time covariates which should have the same length as X.
`Tgrid`	a sequence of times used to perform the cross validation (can be any sequence in the interval `[min(t) , max(t)]` ).
`hgrid`	a sequence of values from which the bandwidth is selected.
`pcv`	a probability value which determines the level of quantiles used to perform the cross validation, with default 0.99.
`kernel`	a kernel function used to compute the weights in the time domain, with default the truncated gaussian kernel.
`kpar`	a value for the kernel function parameter, with no default value.
`CritVal`	a critical value associated to the kernel function computed from the function `CriticalValue`, with default 3.6 corresponding to the truncated Gaussian kernel.
`plot`	If `TRUE`, the cross validation function is plotted.

The sequence hgrid must be geometric. (see bandwidth.grid to generate a geometric grid of bandwidths).

The value pcv should be scalar (vector values are not admitted).

`hgrid`	the sequence of bandwidth given in input.
`CV`	the values of the cross validation function for `hgrid`.
`h.cv`	the bandwidth that minimizes the cross-validation function.

Durrieu, G., Grama, I., Jaunatre, K., Pham, Q. and Tricot, J.- M

Durrieu, G. and Grama, I. and Pham, Q. and Tricot, J.- M (2015). Nonparametric adaptive estimator of extreme conditional tail probabilities quantiles. Extremes, 18, 437-478.

bandwidth.grid , CriticalValue

#Generate the data
theta <- function(t){
   0.5+0.25*sin(2*pi*t)
 }
n <- 5000
t <- 1:n/n
Theta <- theta(t)
Data <- NULL
for(i in 1:n){
   Data[i] <- rparetomix(1, a = 1/Theta[i], b = 1/Theta[i]+5, c = 0.75)
 }

#compute the cross validation bandwidth
Tgrid <- seq(0, 1, 0.02) #define a grid to perform the cross validation
hgrid <- bandwidth.grid(0.1, 0.3, 20) #define a grid of bandwidths
## Not run:  #For computation time purpose
  Hcv <- bandwidth.CV(Data, t, Tgrid, hgrid, pcv = 0.99, plot = TRUE)
  #The computing time can be long
  Hcv

## End(Not run)