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inst/doc/Replicate_literature_results_using_spINAR.R
In spINAR: (Semi)Parametric Estimation and Bootstrapping of INAR Models
## ---- include = FALSE---------------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
## ----setup--------------------------------------------------------------------
library(spINAR)
## -----------------------------------------------------------------------------
# Load the package
library(spINAR)
## -----------------------------------------------------------------------------
ice <- c(0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2,
3, 2, 1, 0, 1, 1, 0, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 1,
2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1,
0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 5, 1, 2, 0, 0, 0,
1, 2, 0, 1, 1, 3, 2, 3, 1, 2, 3, 2, 1, 1, 1, 1, 2, 0, 1, 0, 0, 1, 1, 1,
2, 3, 1, 1, 1, 2, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 1, 1, 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1,
0, 2, 1, 1, 2, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 1, 0, 1, 0, 3, 1, 1, 2, 0,
0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2,
2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0,
1, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 3, 4, 4, 4, 3, 3, 3, 2, 1, 2, 2,
2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1,
1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 2,
2, 1, 1, 1, 0, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 3, 2, 2,
2, 1, 2, 1, 0, 1, 1, 1, 0, 0, 4, 3, 2, 1, 3, 1, 0, 1, 0, 0, 1, 0, 0, 0,
1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1,
2, 2, 2, 0, 0, 0, 1, 3, 1, 2, 1, 0, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 0, 1,
0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
1, 1, 1, 1, 2, 3, 2, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1,
0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1,
1, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 0, 0,
0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 2, 0, 1,
1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2,
1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3, 3, 5,
1, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1,
1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3,
1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 3, 3, 3, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 1,
1, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 4, 3, 2, 0, 2,
2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 4, 2, 1, 0, 1, 3, 1, 0, 1, 0, 0, 0, 0, 1,
1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0,
2, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0,
1, 2, 3, 2, 2, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0,
0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 4, 1, 2, 1, 1, 3,
2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 1, 1, 1, 4, 0, 2, 2, 3, 1, 1, 1, 1, 2, 0, 3, 3, 2, 1, 1,
1, 1, 0, 2, 2, 2, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 0, 1,
1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0,
0, 2, 0, 4, 2, 2, 0, 1, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,
3, 4, 5, 4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 0, 0, 1,
1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1,
0, 3, 1, 2, 3, 3, 1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2,
0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 0, 0, 2, 1, 1, 2, 3, 2, 7, 3, 6,
5, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0,
2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0,
2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2,
0, 1, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 3, 1, 1, 1, 0, 1, 1, 1, 2, 1,
2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
## -----------------------------------------------------------------------------
# p=1
xmax <- max(ice)
est_sp_1 <- spinar_est(ice,1)
mu_e_sp_1 <- sum(est_sp_1[-1]*(0:xmax))
sigma2_e_sp_1 <- sum(est_sp_1[-1]*(0:xmax)^2) - mu_e_sp_1^2
c(est_sp_1, mu_e_sp_1,sigma2_e_sp_1)
# p=2
est_sp_2 <- spinar_est(ice,2)
mu_e_sp_2 <- sum(est_sp_2[-(1:2)]*(0:xmax))
sigma2_e_sp_2 <- sum(est_sp_2[-(1:2)]*(0:xmax)^2) - mu_e_sp_2^2
c(est_sp_1, mu_e_sp_2,sigma2_e_sp_2)
## -----------------------------------------------------------------------------
# p=1
est_p_1 <- spinar_est_param(ice,1,"mom","poi")
est_p_1_v <- c(est_p_1[1],dpois(0:xmax,est_p_1[2]))
unname(c(est_p_1_v, est_p_1[2], est_p_1[2]))
# p=2
est_p_2 <- spinar_est_param(ice,2,"mom","poi")
est_p_2_v <- c(est_p_2[1:2],dpois(0:xmax,est_p_2[3]))
unname(c(est_p_2_v, est_p_2[3], est_p_2[3]))
## -----------------------------------------------------------------------------
# Setting of parametrizations (Jentsch and Weiß, 2017)
B <- 10^4
level <- 0.05
M <- 10
mu_est <- mean(ice)
## -----------------------------------------------------------------------------
# p=1
xstar_p <- spinar_boot(ice, 1, B, "p", "mom", "poi", progress = FALSE)$x_star
mu_est_star <- apply(xstar_p, 2, mean)
mu_est_star_cent <- mu_est_star - mu_est
srt <- sort(mu_est_star_cent)
c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
# p=2
xstar_p <- spinar_boot(ice, 2, B, "p", "mom", "poi", progress = FALSE)$x_star
mu_est_star <- apply(xstar_p, 2, mean)
mu_est_star_cent <- mu_est_star - mu_est
srt <- sort(mu_est_star_cent)
c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
## ----eval=FALSE---------------------------------------------------------------
# # p=1
# mu_est_cent <- mu_e_sp_1/(1-est_sp_1[1])
# xstar_sp <- spinar_boot(ice, 1, B, "sp", progress = FALSE)$x_star
# mu_est_star <- apply(xstar_sp, 2, mean)
# mu_est_star_cent <- mu_est_star - mu_est_cent
# srt <- sort(mu_est_star_cent)
# c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
#
# # p=2
# mu_est_cent <- mu_e_sp_2/(1-est_sp_2[1]-est_sp_2[2])
# xstar_sp <- spinar_boot(ice, 2, B, "sp", progress = FALSE)$x_star
# mu_est_star <- apply(xstar_sp, 2, mean)
# mu_est_star_cent <- mu_est_star - mu_est_cent
# srt <- sort(mu_est_star_cent)
# c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
## -----------------------------------------------------------------------------
# Load the data set
data <- c(1,1,0,2,1,4,4,5,4,0,2,1,0,0,1,2,1,3,1,0,1,2,1,0,0,1,0,1,0,0,2,0,2,2,0,
2,1,0,1,2,1,1,0,0,0,0,0,0,1,2,2)
## -----------------------------------------------------------------------------
# Unpenalized estimation of the innovation distribution
est_unpenal <- spinar_est(data,1)
# Penalized estimation of the innovation distribution
est_penal <- spinar_penal(data,1,0,1)
## ----eval=FALSE---------------------------------------------------------------
# par(mfrow=c(1,2))
# barplot(est_unpenal[-1], ylim=c(0,1),names.arg=0:5,
# main="Unpenalized estimated \n innovation distribution")
# barplot(est_penal[-1], ylim=c(0,1),names.arg=0:5,
# main="Penalized estimated \n innovation distribution")
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## ---- include = FALSE---------------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
## ----setup--------------------------------------------------------------------
library(spINAR)
## -----------------------------------------------------------------------------
# Load the package
library(spINAR)
## -----------------------------------------------------------------------------
ice <- c(0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2,
3, 2, 1, 0, 1, 1, 0, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 1,
2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1,
0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 5, 1, 2, 0, 0, 0,
1, 2, 0, 1, 1, 3, 2, 3, 1, 2, 3, 2, 1, 1, 1, 1, 2, 0, 1, 0, 0, 1, 1, 1,
2, 3, 1, 1, 1, 2, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 1, 1, 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1,
0, 2, 1, 1, 2, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 1, 0, 1, 0, 3, 1, 1, 2, 0,
0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2,
2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0,
1, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 3, 4, 4, 4, 3, 3, 3, 2, 1, 2, 2,
2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1,
1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 2,
2, 1, 1, 1, 0, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 3, 2, 2,
2, 1, 2, 1, 0, 1, 1, 1, 0, 0, 4, 3, 2, 1, 3, 1, 0, 1, 0, 0, 1, 0, 0, 0,
1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1,
2, 2, 2, 0, 0, 0, 1, 3, 1, 2, 1, 0, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 0, 1,
0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
1, 1, 1, 1, 2, 3, 2, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1,
0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1,
1, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 0, 0,
0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 2, 0, 1,
1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2,
1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 3, 3, 5,
1, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1,
1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3,
1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 3, 3, 3, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 1,
1, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 4, 3, 2, 0, 2,
2, 2, 0, 2, 2, 2, 2, 0, 1, 2, 4, 2, 1, 0, 1, 3, 1, 0, 1, 0, 0, 0, 0, 1,
1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0,
2, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0,
1, 2, 3, 2, 2, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 2, 2, 0,
0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 4, 1, 2, 1, 1, 3,
2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 1, 1, 1, 4, 0, 2, 2, 3, 1, 1, 1, 1, 2, 0, 3, 3, 2, 1, 1,
1, 1, 0, 2, 2, 2, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 0, 1,
1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0,
0, 2, 0, 4, 2, 2, 0, 1, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,
3, 4, 5, 4, 4, 3, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 0, 0, 1,
1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1,
0, 3, 1, 2, 3, 3, 1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2,
0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 0, 0, 2, 1, 1, 2, 3, 2, 7, 3, 6,
5, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0,
2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0,
2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2,
0, 1, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 3, 1, 1, 1, 0, 1, 1, 1, 2, 1,
2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
## -----------------------------------------------------------------------------
# p=1
xmax <- max(ice)
est_sp_1 <- spinar_est(ice,1)
mu_e_sp_1 <- sum(est_sp_1[-1]*(0:xmax))
sigma2_e_sp_1 <- sum(est_sp_1[-1]*(0:xmax)^2) - mu_e_sp_1^2
c(est_sp_1, mu_e_sp_1,sigma2_e_sp_1)
# p=2
est_sp_2 <- spinar_est(ice,2)
mu_e_sp_2 <- sum(est_sp_2[-(1:2)]*(0:xmax))
sigma2_e_sp_2 <- sum(est_sp_2[-(1:2)]*(0:xmax)^2) - mu_e_sp_2^2
c(est_sp_1, mu_e_sp_2,sigma2_e_sp_2)
## -----------------------------------------------------------------------------
# p=1
est_p_1 <- spinar_est_param(ice,1,"mom","poi")
est_p_1_v <- c(est_p_1[1],dpois(0:xmax,est_p_1[2]))
unname(c(est_p_1_v, est_p_1[2], est_p_1[2]))
# p=2
est_p_2 <- spinar_est_param(ice,2,"mom","poi")
est_p_2_v <- c(est_p_2[1:2],dpois(0:xmax,est_p_2[3]))
unname(c(est_p_2_v, est_p_2[3], est_p_2[3]))
## -----------------------------------------------------------------------------
# Setting of parametrizations (Jentsch and Weiß, 2017)
B <- 10^4
level <- 0.05
M <- 10
mu_est <- mean(ice)
## -----------------------------------------------------------------------------
# p=1
xstar_p <- spinar_boot(ice, 1, B, "p", "mom", "poi", progress = FALSE)$x_star
mu_est_star <- apply(xstar_p, 2, mean)
mu_est_star_cent <- mu_est_star - mu_est
srt <- sort(mu_est_star_cent)
c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
# p=2
xstar_p <- spinar_boot(ice, 2, B, "p", "mom", "poi", progress = FALSE)$x_star
mu_est_star <- apply(xstar_p, 2, mean)
mu_est_star_cent <- mu_est_star - mu_est
srt <- sort(mu_est_star_cent)
c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
## ----eval=FALSE---------------------------------------------------------------
# # p=1
# mu_est_cent <- mu_e_sp_1/(1-est_sp_1[1])
# xstar_sp <- spinar_boot(ice, 1, B, "sp", progress = FALSE)$x_star
# mu_est_star <- apply(xstar_sp, 2, mean)
# mu_est_star_cent <- mu_est_star - mu_est_cent
# srt <- sort(mu_est_star_cent)
# c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
#
# # p=2
# mu_est_cent <- mu_e_sp_2/(1-est_sp_2[1]-est_sp_2[2])
# xstar_sp <- spinar_boot(ice, 2, B, "sp", progress = FALSE)$x_star
# mu_est_star <- apply(xstar_sp, 2, mean)
# mu_est_star_cent <- mu_est_star - mu_est_cent
# srt <- sort(mu_est_star_cent)
# c(mu_est - quantile(srt,1-level,names=FALSE), mu_est - quantile(srt,level,names=FALSE))
## -----------------------------------------------------------------------------
# Load the data set
data <- c(1,1,0,2,1,4,4,5,4,0,2,1,0,0,1,2,1,3,1,0,1,2,1,0,0,1,0,1,0,0,2,0,2,2,0,
2,1,0,1,2,1,1,0,0,0,0,0,0,1,2,2)
## -----------------------------------------------------------------------------
# Unpenalized estimation of the innovation distribution
est_unpenal <- spinar_est(data,1)
# Penalized estimation of the innovation distribution
est_penal <- spinar_penal(data,1,0,1)
## ----eval=FALSE---------------------------------------------------------------
# par(mfrow=c(1,2))
# barplot(est_unpenal[-1], ylim=c(0,1),names.arg=0:5,
# main="Unpenalized estimated \n innovation distribution")
# barplot(est_penal[-1], ylim=c(0,1),names.arg=0:5,
# main="Penalized estimated \n innovation distribution")
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