b.BO.MBC {DOvalidation}

Best One-Sided Cross-Validation for Multiplicative Bias Corrected Hazard Estimators

Description

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

Usage

b.BO.MBC(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 hazard. Choose between values "epa" (for the Epanechnikov kernel) or "sextic" (see details of hazard.MBC 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.

Details

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 0.5948 for the Epanechnikov kernel, and 0.6501 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).

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.

Author(s)

Gamiz, M.L., Martinez-Miranda, M.D. and Nielsen, J.P.

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.MBC,b.OSCV.MBC,b.CV.MBC

Examples

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(50,80,length.out=30)
res.bo<-b.BO.MBC(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=" "))