DefVarBandRule: Default adaptive bandwidth rule
In NPHazardRate: Nonparametric Hazard Rate Estimation

Description Usage Arguments Details Value References See Also Examples

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

1	DefVarBandRule(xin, cens)

`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.

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

h_2 = ≤ft [ \frac{R(K) M_2}{8nμ_4^2(K) R(g)} \right ]^{1/14}

where

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

and

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

the value of the adaptive bandwidth

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

HazardRateEst, TransHazRateEst, PlugInBand

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