DOvalidation (version 1.1.0)

b.BO: Best One-Sided Cross-Validation for Local Linear Hazards

Description

Bandwidth selection for local linear hazard estimation using best one-sided cross-validation

Usage

b.BO(grid.b, nb , K = "sextic", type.bo = "Oi", xi, Oi, Ei, wei = "same")

Arguments

grid.b

Optional. A vector of bandwidths to minimise the cross-validation score. If not specified it will be considered an equally-spaced grid of nb bandwidths between "amp/(M+1)" and "amp/2" for "amp" being the range of xi and "M" its length.

nb

Optional. The number of bandwidths used to minimise the cross-validation score. If grid.b is provided then the argument nb will be ignored (if specified).

K

Indicates the kernel function to be considered in the local linear hazard estimator. Choose between values "epa" (for the epanechnikov kernel) or "sextic" (see details inhazard.LL for the definition).

type.bo

Choose between "Oi" or "Ei" to find the best side using the occurrences or the exposures, respectively.

xi

Vector of time points where the count data are given.

Oi

Vector with the number (counts) of occurrences observed at each time point (xi).

Ei

Vector with the observed exposure at each time point (xi).

wei

Indicates the weights used in the cross-validation score. Choose between the value "exposure" or "same". See details below.

Value

bbo

The onesided cross-validated bandwidth.

ind.bo

The position of the best one-sided cross-validated bandwidth into "grid.b".

cvbo.values

The values of the cross-validation score for each bandwidth in grid.b.

b.grid

The grid of bandwidths where the score has been evaluated.

Details

It is assumed that the data are given as count data i.e. number of occurrences and exposures.

The BO-validated bandwidth is calculated as the minimizer of a cross-validation score with a indirect kernel. If the score is strictly increasing or decreasing then a warning will be shown together with the selected bandwidth (in this case one of the extremes in grid.b, adjusted by the rescaling constant, which is 0.5371 for the Epanechnikov kernel, and 0.5874 for the sextic kernel).

The score is defined with two different weighting functions. This is controlled with the parameter wei. By default wei="exposure" that means that only areas where the exposure is significant contribute to the criterion. Specify wei="same" to allow all time points contribute the same to the criterion (see Gamiz et al. 2017).

References

Gamiz, M.L., Martinez-Miranda, M.D. and Nielsen, J.P. (2017). Multiplicative local linear hazard estimation and best one-sided cross-validation. Available at http://arxiv.org/abs/1710.05575

Nielsen, J.P. and Tanggaard, C. (2001). Boundary and bias correction in kernel hazard estimation. Scandinavian Journal of Statistics,28, 675-698.

See Also

hazard.LL,b.OSCV,b.CV

Examples

# NOT RUN {
data(Iceland)
Oi<-Iceland$D
Ei<-Iceland$E
ti<-40:110  # time is age and it goes from 40 to 110 years
my.bs<-seq(20,40,length.out=30)
res.bo<-b.BO(grid.b=my.bs,K="sextic",type.bo="Oi",xi=ti,Oi=Oi,Ei=Ei,wei="same")
bbo<-res.bo$bbo
cvs<-res.bo$cvbo.values
plot(my.bs,cvs,main="BO-validation score",xlab="Bandwidth")
print(paste("The best one-sided cross-validated bandwidth is:", bbo,sep=" "))
# }