mllRH2: Minus loglikelihood of a RHawkes model with Rosenblatt residuals

Description

Calculates the minus loglikelihood of a RHawkes model with given immigration hazard function \(\mu\), offspring density function \(h\) and branching ratio \(\eta\) for event times tms on interval \([0,cens]\). The same as mllRH although this version also returns the Rosenblatt residuals.

Usage

mllRH2(tms, cens, par, h.fn = function(x, p) dexp(x, rate = 1/p), 
       mu.fn = function(x, p) {
         exp(dweibull(x, shape = p[1], scale = p[2], log = TRUE) - 
         pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE))}, 
       H.fn = function(x, p) pexp(x, rate = 1/p), 
       Mu.fn = function(x, p) {
         -pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE)
       })

Arguments

tms

A numeric vector, with values sorted in ascending order. Event times to fit the RHawkes point process model.

cens

A scalar. The censoring time.

par

A numeric vector containing the parameters of the model, in order of the immigration parameters \(\mu(.)\), offspring parameters \(h(.)\) and lastly the branching ratio \(\eta(.)\).

h.fn

A (vectorized) function. The offspring density function.

mu.fn

A (vectorized) function. The immigration hazard function.

H.fn

A (vectorized) function. Its value at t gives the integral of the offspring density function from 0 to t.

Mu.fn

A (vectorized) function. Its value at t gives the integral of the immigrant hazard function from 0 to t.

Value

mll

minus log-likelihood

Rosenblatt residual of observed event time

number of events

Details

Calculate the RHawkes point process Rosenblatt residuals

Examples

Run this code

# NOT RUN {
tmp <- mllRH2(sort(runif(1000,0,1000)),1001,c(2,1,0.5,1))
par(mfrow=c(1,2))
qqunif<-function(dat,...){
  dat<-sort(as.numeric(dat));
  n<-length(dat);
  pvec<-ppoints(n);
  plot(pvec,dat,xlab="Theoretical Quantiles",
       ylab="Sample Quantiles",main="Uniform Q-Q Plot",...)
}
qqunif(tmp$U)
acf(tmp$U)
ks.test(tmp$U,"punif")
# }