HazardHistogram {NPHazardRate}

Histogram Hazard Rate Estimator

Description

Implements the histogram hazard rate estimator of Patil and Bagkavos (2012)

Usage

HazardHistogram(xin, xout, cens, bin)

Arguments

xin

A vector of data points. Missing values not allowed.

xout

A vector of grid points at which the histogram will be calculated.

cens

A vector of 1s and zeros, 1's indicate uncensored observations, 0's correspond to censored obs.

bin

Number of bins to use in construction of the histogram.

Details

The histogram hazard rate estimator is defined in (1), Patil and Bagkavos (2012) by

\hat \lambda (x) = h_n^{-1} C_{i_{(x)}} = h_n^{-1}f_{i_{(x)}}^0(\bar F_{i_{(x)}}+1)^{-1}.

Value

A vector with the values of the histogram estimate at each bin.

References

Patil and Bagkavos (2012), Histogram for hazard rate estimation, pp. 286-301, Sankhya, B.

Examples

SampleSize <-400
ti<-rweibull(SampleSize,0.5,0.8)
xout<-seq(0.02, 3.5, length=80)
true.hazard<-dweibull(xout,0.5, 0.8)/(1-pweibull(xout, 0.5, 0.8))
cen<-rep.int(1, SampleSize)
cen[sample(1:SampleSize, SampleSize/10)]<-0

band<-nlminb(start= 2, obj=cvfunction, control = list(iter.max = 100, x.tol = .001)
            ,xin=ti, xout= xout, cens = cen, 	lower=.01, upper=max(xout))
bin<- 3.49 * sd(ti)^2 * SampleSize^(-1/3) /50 #Scott 1979 Biometrika default rule
bin<-unlist(band[1])
histest<- HazardHistogram(ti,xout, cen, bin+0.013 )

plot(xout, true.hazard, type="l")
lines(histest[,1], histest[,2], col=2, type="s")
barplot( histest[,2], rep(bin, times=length(histest[,2])))
lines(xout, true.hazard, type="l", lwd=2, col=2)