DefVarBandRule {NPHazardRate}

Default adaptive bandwidth rule

Description

Implements an adaptive variable bandwidth hazard rate rule for use with the VarBandHazEst based on the Weibull distribution, with parameters estimated by maximum likelihood

Usage

DefVarBandRule(xin, cens)

Arguments

xin

A vector of data points. Missing values not allowed.

cens

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

Details

The adaptive AMISE optimal bandwidth for the variable bandwidth hazard rate estimator VarBandHazEst is given by

h_2 = \left [ \frac{R(K) M_2}{8n\mu_4^2(K) R(g)} \right ]^{1/14}

where

M_2 = \int \frac{\lambda^{3/2}(x)}{1-F(x)} \,dx

and

g(x)=\frac{1}{24\lambda(x)^5} \Bigl (24{\lambda'(x)}^4-36{\lambda'(x)}^2{\lambda''(x)}^2\lambda(x)+6{\lambda''(x)}^2\lambda^2(x) + 8\lambda'(x)\lambda'''(x)\lambda^2(x) -\lambda^{(4)}(x)\lambda^3(x)\Bigr )

Value

the value of the adaptive bandwidth

References

Bagkavos and Patil (2009), Variable Bandwidths for Nonparametric Hazard Rate Estimation, Communications in Statistics - Theory and Methods, 38:7, 1055-1078

See Also

HazardRateEst, TransHazRateEst, PlugInBand

Examples

library(survival)
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, .05)       #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

h2<-DefVarBandRule(ti, cen)     #Deafult Band. Rule - Weibull Reference