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#' Most recent changepoint using ind method
#'
#' @description Analyzing each series in the panel independently (IND)
#' method that is the simplest one to analyze all the series independently
#' in the panel data and in each given series estimate the most recent
#' changepoint. We use PELT for segmenting a time series into changing
#' means, assumes normally distributed observations
#' with changing mean but constant variance
#' @param data a censored data matrix
#' @param pen (penalty term) default 2*log(n). If pen is equal to zero, penalty term will be equal
#' to 2*log(n)
#'@return indicates the most recent changepoint in each series .
#'@export
#' @examples
#' #Default example
#'library(cpcens)
#'data("censoredex")
#'data=censoredex
#'n=144
#'N=100
#' out=ind(data, pen=0)
ind = function( data,pen=0 ){
n = dim(data)[2]
N = dim(data)[1]
icp = numeric(N)
for (j in 1:N){
cpts = PELT(data[j,],2*log(n))$cpts
icp[j] = cpts[length(cpts)]
}
return( icp )
}
PELT <- function(data,pen){
n = length(data)
# if unspecified penalty make it BIC
if (pen==0){
pen = 2*log(n)
}
# F[t] = optimal value of segmentation upto time t
F = numeric(n+1)
F[1:2] = c(-pen,0)
# chpts[[t]] = a vector of changepoints upto time t (optimal)
chpts = vector("list",n+1)
chpts[[1]] = NULL
chpts[[2]]= c(0)
R = c(0,1)
# useful for calculating seg costs
cd = cumsum(c(0,data))
cd_2 = cumsum(c(0,data^2) )
for (t in 2:n){
cpt_cands = R
seg_costs = cd_2[t+1] - cd_2[cpt_cands+1] - ((cd[t+1] - cd[cpt_cands+1])^2/(t-cpt_cands))
f = F[cpt_cands+1] + seg_costs + pen
F[t+1] = min(f)
tau = cpt_cands[ which.min(f) ]
chpts[[t+1]] = c( chpts[[ tau+1 ]] , tau )
# pruning step
ineq_prune = F[cpt_cands+1] + seg_costs <= F[t+1]
R = c( cpt_cands[ineq_prune] , t )
}
# if only a single chpt detected at 1 then no changepoint in series, i.e., 0.
cpts = chpts[[n+1]]
newList <- list("cpts" = cpts , "F" = F )
return(newList)
}
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