HazardRateEst {NPHazardRate}

Kernel Hazard Rate Estimation

Description

Implements the (classical) kernel hazard rate estimator for right censored data defined in Tanner and Wong (1983).

Usage

HazardRateEst(xin, xout, kfun, h, ci)

Arguments

xin

A vector of data points. Missing values not allowed.

xout

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

kfun

Kernel function to use. Supported kernels: Epanechnikov, Biweight, Gaussian, Rectangular, Triangular, HigherOrder.

h

A scalar, the bandwidth to use in the estimate.

ci

A vector of censoring indicators: 1's indicate uncensored observations, 0's correspond to censored obs.

Details

The kernel hazard rate estimator of Tanner and Wong (1983) is given by

\hat \lambda(x;h) = \sum_{i=1}^n \frac{K_h(x-X_{(i)})\delta_{(i)}}{n-i+1}

h is determined by a bandwidth rule such as PlugInBand. HazardRateEst is also used as a pilot estimate in the implementation of both the variable bandwidth estimate VarBandHazEst and the transformed hazard rate estimate TransHazRateEst.

Value

A vector with the hazard rate estimates at the designated points xout.

References

Tanner and Wong (1983), The Estimation Of The Hazard Function From Randomly Censored Data By The Kernel Method, Annals of Statistics, 3, pp. 989-993.

See Also

VarBandHazEst, TransHazRateEst, PlugInBand

Examples

x<-seq(0, 5,length=100) #design points where the estimate will be calculated
plot(x, HazardRate(x, "weibull", .6, 1),  type="l", xlab = "x",
                   ylab="Hazard rate") #plot true hazard rate function
SampleSize <- 100
ti<- rweibull(SampleSize, .6, 1)  #draw a random sample from the actual distribution
ui<-rexp(SampleSize, .2)  #draw a random sample from the censoring distribution
cat("\n AMOUNT OF CENSORING: ", length(which(ti>ui))/length(ti)*100, "\n")
x1<-pmin(ti,ui)             #this is the observed sample
cen<-rep.int(1, SampleSize) #censoring indicators
cen[which(ti>ui)]<-0        #censored values correspond to zero
huse<-PlugInBand(x1, x,   cen, Biweight)
arg2<-HazardRateEst(x1, x, Epanechnikov, huse, cen) #Calculate the estimate
lines(x, arg2, lty=2)       #draw the result on the graphics device.