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8_Finite_REDSs_imomentRMSEcalibration.R
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8_Finite_REDSs_imomentRMSEcalibration.R
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#Copyright 2023 Tuobang Li
#These codes and manuscripts are under review in PNAS, please do not share them.
#If you are interested, please do not hesitate to contact me. Cooperation is also welcomed!
#require foreach and doparallel for parallel processing of bootstrap (not available for some types of computers)
if (!require("foreach")) install.packages("foreach")
library(foreach)
if (!require("doParallel")) install.packages("doParallel")
library(doParallel)
#require randtoolbox for random number generations
if (!require("randtoolbox")) install.packages("randtoolbox")
library(randtoolbox)
if (!require("Rcpp")) install.packages("Rcpp")
library(Rcpp)
if (!require("Rfast")) install.packages("Rfast")
library(Rfast)
if (!require("REDSReview")) install.packages("REDSReview_1.0.tar.gz", repos = NULL)
library(REDSReview)
if (!require("matrixStats")) install.packages("matrixStats")
library(matrixStats)
numCores <- detectCores()-4 # Detect the number of available cores
cl <- makeCluster(numCores) # Create a cluster with the number of cores
registerDoParallel(cl) # Register the parallel backend
#bootsize for bootstrap approximation of the distributions of the kernal of U-statistics.
n <- 13824*2*3
(n%%10)==0
# maximum order of moments
morder <- 4
#large sample size (approximating asymptotic)
largesize<-13824*2
#generate quasirandom numbers based on the Sobol sequence
quasiunisobol<-sobol(n=n, dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
quasiuni<-quasiunisobol
quasiuni_sorted2 <- na.omit(rowSort(quasiuni[,1:2], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted3 <- na.omit(rowSort(quasiuni[,1:3], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted4 <- na.omit(rowSort(quasiuni, descend = FALSE, stable = FALSE, parallel = TRUE))
# Forever...
#load asymptotic d for two parameter distributions
#set the stop criterion
criterionset=1e-10
kurtlognorm<- read.csv(("kurtlognorm_31180.csv"))
allkurtlognorm<-unlist(kurtlognorm)
samplesize=576*9
batchsizebase=1000
orderlist1_AB20<-createorderlist(quni1=quasiuni_sorted2,size=samplesize,interval=8,dimension=2)
orderlist1_AB20<-orderlist1_AB20[1:largesize,]
orderlist1_AB30<-createorderlist(quni1=quasiuni_sorted3,size=samplesize,interval=8,dimension=3)
orderlist1_AB30<-orderlist1_AB30[1:largesize,]
orderlist1_AB40<-createorderlist(quni1=quasiuni_sorted4,size=samplesize,interval=8,dimension=4)
orderlist1_AB40<-orderlist1_AB40[1:largesize,]
batchsize=batchsizebase
n <- samplesize
setSeed(1)
unibatchran<-matrix(SFMT(samplesize*batchsize),ncol=batchsize)
unibatch<-colSort(unibatchran, descend = FALSE, stable = FALSE, parallel = TRUE)
#input the d value table previously generated
d_values<- read.csv(("d_values.csv"))
I_values<-read.csv(("I_values.csv"))
Ismoments_values<-read.csv(("Ismoments_values.csv"))
#Then, start the Monte Simulation
generate_indices <- function(start, end, step = 192,step2=71) {
indices <- c()
for (i in seq(start, end, step)) {
indices <- c(indices, seq(i, i + step2))
}
return(indices)
}
simulatedbatch_bias_Monte<-foreach(batchnumber =c((1:length(allkurtlognorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
set.seed(1)
a=allkurtlognorm[batchnumber]
targetm<-exp((a^2)/2)
targetvar<-(exp((a/1)^2)*(-1+exp((a/1)^2)))
targettm<-sqrt(exp((a/1)^2)-1)*((2+exp((a/1)^2)))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^3)
targetfm<-((-3+exp(4*((a/1)^2))+2*exp(3*((a/1)^2))+3*exp(2*((a/1)^2))))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^4)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
RMSEbataches<- read.csv(paste("finite_lognorm_Icalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
RMSEbataches2<- read.csv(paste("finite_lognorm_Ismomentscalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
RMSEbataches3<-c()
for (batch1 in c(1:batchsize)){
iall11<-RMSEbataches[batch1,]
iall12<-RMSEbataches2[batch1,]
x<-c(dslnorm(uni=unibatch[,batch1], meanlog =0, sdlog = a/1))
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
rqmomentselect1<-rqmoments3(x=sortedx,iall1=iall11,dtype1=1,Iskewtype1 = 4,Ikurttype1 = 4,releaseall=TRUE,standist_d=d_values,orderlist1_sorted20=orderlist1_AB20,orderlist1_sorted30=orderlist1_AB30,orderlist1_sorted40=orderlist1_AB40,percentage=1/24,batch="auto",stepsize=50,criterion=1e-10,boot=TRUE)
standardizedmomentsx<-standardizedmoments(x=sortedx)
sortedx<-c()
all1<-(c(rqmomentselect1,targetall,standardizedmomentsx))
RMSEbataches3<-rbind(RMSEbataches3,all1)
}
write.csv(RMSEbataches3,paste("finite_lognorm_Imomentscalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","), row.names = FALSE)
RMSEbatachesmean <-apply(RMSEbataches3, 2, calculate_column_mean)
rqmean<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=1, end=1729, step = 192,step2=71))]-targetm)^2))
rqvar<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=73, end=1801, step = 192,step2=51))]-targetvar)^2))
rqtm<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=125, end=1853, step = 192,step2=39))]-targettm)^2))
rqfm<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=165, end=1893, step = 192,step2=27))]-targetfm)^2))
rankmean1<-rank(rqmean)
rankvar1<-rank(rqvar)
ranktm1<-rank(rqtm)
rankfm1<-rank(rqfm)
allresultsSE<-c(samplesize=samplesize,type=4,kurtx,skewx,rankmean1,rankvar1,ranktm1,rankfm1,RMSEbatachesmean,RMSErqmean=rqmean,RMSErqvar=rqvar,RMSErqtm=rqtm,RMSErqfm=rqfm)
}
write.csv(simulatedbatch_bias_Monte,paste("finite_lognorm_Imomentscalibration_raw",samplesize,".csv", sep = ","), row.names = FALSE)
Optimum_RMSE<-simulatedbatch_bias_Monte[,1:(1924)]
write.csv(Optimum_RMSE,paste("finite_Imoments_lognorm.csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte_SE<-foreach(batchnumber =c((1:length(allkurtlognorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
a=allkurtlognorm[batchnumber]
targetm<-exp((a^2)/2)
targetvar<-(exp((a/1)^2)*(-1+exp((a/1)^2)))
targettm<-sqrt(exp((a/1)^2)-1)*((2+exp((a/1)^2)))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^3)
targetfm<-((-3+exp(4*((a/1)^2))+2*exp(3*((a/1)^2))+3*exp(2*((a/1)^2))))*((sqrt(exp((a/1)^2)*(-1+exp((a/1)^2))))^4)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<- read.csv(paste("finite_lognorm_Imomentscalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
se_mean_all1<-apply((SEbataches[1:batchsize,]), 2, se_mean)
rqmean_se<-apply(((SEbataches[1:batchsize,c(generate_indices(start=1, end=1729, step = 192,step2=71))])), 2, se_sd)
rqvar_se<-apply((SEbataches[1:batchsize,c(generate_indices(start=73, end=1801, step = 192,step2=51))]), 2, se_sd)
rqtm_se<-apply((SEbataches[1:batchsize,c(generate_indices(start=125, end=1853, step = 192,step2=39))]), 2, se_sd)
rqfm_se<-apply((SEbataches[1:batchsize,c(generate_indices(start=165, end=1893, step = 192,step2=27))]), 2, se_sd)
allresultsSE<-c(samplesize=samplesize,type=4,kurtx,skewx,se_mean_all1,rqmean_se,rqvar_se,rqtm_se,rqfm_se)
allresultsSE
}
write.csv(simulatedbatch_bias_Monte_SE,paste("finite_lognorm_Imomentscalibration_raw_error",samplesize,".csv", sep = ","), row.names = FALSE)
kurtgnorm<- read.csv(("kurtgnorm_21180.csv"))
allkurtgnorm<-unlist(kurtgnorm)
simulatedbatch_bias_Monte<-foreach(batchnumber =c((1:length(allkurtgnorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
set.seed(1)
a=allkurtgnorm[batchnumber]
targetm<-0
targetvar<-gamma(3/a)/((gamma(1/a)))
targettm<-0
targetfm<-((gamma(3/a)/((gamma(1/a))))^2)*gamma(5/a)*gamma(1/a)/((gamma(3/a))^2)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
RMSEbataches<- read.csv(paste("finite_gnorm_Icalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
RMSEbataches2<- read.csv(paste("finite_gnorm_Ismomentscalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
RMSEbataches3<-c()
for (batch1 in c(1:batchsize)){
iall11<-RMSEbataches[batch1,]
iall12<-RMSEbataches2[batch1,]
x<-c(dsgnorm(uni=unibatch[,batch1], shape=a/1, scale = 1))
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
rqmomentselect1<-rqmoments3(x=sortedx,iall1=iall11,dtype1=1,Iskewtype1 = 4,Ikurttype1 = 4,releaseall=TRUE,standist_d=d_values,orderlist1_sorted20=orderlist1_AB20,orderlist1_sorted30=orderlist1_AB30,orderlist1_sorted40=orderlist1_AB40,percentage=1/24,batch="auto",stepsize=50,criterion=1e-10,boot=TRUE)
standardizedmomentsx<-standardizedmoments(x=sortedx)
sortedx<-c()
all1<-(c(rqmomentselect1,targetall,standardizedmomentsx))
RMSEbataches3<-rbind(RMSEbataches3,all1)
}
write.csv(RMSEbataches3,paste("finite_gnorm_Imomentscalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","), row.names = FALSE)
RMSEbatachesmean <-apply(RMSEbataches3, 2, calculate_column_mean)
rqmean<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=1, end=1729, step = 192,step2=71))]-targetm)^2))
rqvar<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=73, end=1801, step = 192,step2=51))]-targetvar)^2))
rqtm<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=125, end=1853, step = 192,step2=39))]-targettm)^2))
rqfm<-sqrt(colMeans((RMSEbataches3[1:batchsize,c(generate_indices(start=165, end=1893, step = 192,step2=27))]-targetfm)^2))
rankmean1<-rank(rqmean)
rankvar1<-rank(rqvar)
ranktm1<-rank(rqtm)
rankfm1<-rank(rqfm)
allresultsSE<-c(samplesize=samplesize,type=5,kurtx,skewx,rankmean1,rankvar1,ranktm1,rankfm1,RMSEbatachesmean,RMSErqmean=rqmean,RMSErqvar=rqvar,RMSErqtm=rqtm,RMSErqfm=rqfm)
}
write.csv(simulatedbatch_bias_Monte,paste("finite_gnorm_Imomentscalibration_raw",samplesize,".csv", sep = ","), row.names = FALSE)
Optimum_RMSE<-simulatedbatch_bias_Monte[,1:(1924)]
write.csv(Optimum_RMSE,paste("finite_Imoments_gnorm.csv", sep = ","), row.names = FALSE)
simulatedbatch_bias_Monte_SE<-foreach(batchnumber =c((1:length(allkurtgnorm))), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
a=allkurtgnorm[batchnumber]
targetm<-0
targetvar<-gamma(3/a)/((gamma(1/a)))
targettm<-0
targetfm<-((gamma(3/a)/((gamma(1/a))))^2)*gamma(5/a)*gamma(1/a)/((gamma(3/a))^2)
kurtx<-targetfm/(targetvar^(4/2))
skewx<-targettm/(targetvar^(3/2))
SEbataches<- read.csv(paste("finite_gnorm_Imomentscalibration_raw",samplesize,round(kurtx,digits = 1),".csv", sep = ","))
se_mean_all1<-apply((SEbataches[1:batchsize,]), 2, se_mean)
rqmean_se<-apply(((SEbataches[1:batchsize,c(generate_indices(start=1, end=1729, step = 192,step2=71))])), 2, se_sd)
rqvar_se<-apply((SEbataches[1:batchsize,c(generate_indices(start=73, end=1801, step = 192,step2=51))]), 2, se_sd)
rqtm_se<-apply((SEbataches[1:batchsize,c(generate_indices(start=125, end=1853, step = 192,step2=39))]), 2, se_sd)
rqfm_se<-apply((SEbataches[1:batchsize,c(generate_indices(start=165, end=1893, step = 192,step2=27))]), 2, se_sd)
allresultsSE<-c(samplesize=samplesize,type=5,kurtx,skewx,se_mean_all1,rqmean_se,rqvar_se,rqtm_se,rqfm_se)
allresultsSE
}
write.csv(simulatedbatch_bias_Monte_SE,paste("finite_gnorm_Imomentscalibration_raw_error",samplesize,".csv", sep = ","), row.names = FALSE)
finite_I_gnorm<-( read.csv(("finite_Imoments_gnorm.csv")))
finite_I_lognorm<-( read.csv(("finite_Imoments_lognorm.csv")))
names(finite_I_lognorm)<-1:ncol(finite_I_lognorm)
names(finite_I_gnorm)<-1:ncol(finite_I_lognorm)
finite_I_lognorm<-rbind(finite_I_lognorm,finite_I_gnorm)
finite_I_gnorm<- read.csv(("finite_Imoments_lognorm.csv"))
names(finite_I_lognorm)<-names(finite_I_gnorm)
asymptotic_I_lognorm<- read.csv(paste("asymptotic_Imoments.csv", sep = ","))
colnames(finite_I_lognorm)<-colnames(asymptotic_I_lognorm)
all1<-rbind(asymptotic_I_lognorm,finite_I_lognorm)
finite_I_lognorm<-data.frame(finite_I_lognorm)
asymptotic_I_lognorm<- read.csv(paste("asymptotic_Imoments.csv", sep = ","))
colnames(asymptotic_I_lognorm)<-colnames(finite_I_lognorm)
all1<-rbind(asymptotic_I_lognorm,finite_I_lognorm)
write.csv(all1,paste("Imoments_values.csv", sep = ","), row.names = FALSE)
stopCluster(cl)
registerDoSEQ()