iHazardRateEst {NPHazardRate}

Kernel Integrated Hazard Rate Estimation

Description

Implements the integrated kernel hazard rate estimator for right censored data, i.e. a kernel estimate of the cummulative hazard function.

Usage

iHazardRateEst(xin, xout, ikfun, h, ci)

Arguments

xin

A vector of data points. Missing values not allowed.

xout

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

ikfun

Integrated kernel function to use

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 function iHazardRateEst implements the cummulative hazard rate estimator \hat \Lambda(x; h_1) given by

\hat \Lambda(x; h_1) = \sum_{i=1}^n \frac{k\left \{(x-X_{(i)})h_1^{-1}\right \}\delta_{(i)}}{n-i+1}

where

k(x) = \int_{-\infty}^x K(y)\,dy

Note that iHazardRateEst is used in the implementation of the transformed hazard rate estimate TransHazRateEst.

Value

A vector with the cummulative 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

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<-iHazardRateEst(x1, x, IntEpanechnikov, huse, cen) #Calculate the estimate