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REDS_Mean_four_distributions.R
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REDS_Mean_four_distributions.R
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#Copyright 2023 Tuobang Li
#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)
if (!require("rootSolve")) install.packages("rootSolve")
library(rootSolve)
numCores <- detectCores()-4
#registering clusters, can set a smaller number using numCores-1
registerDoParallel(numCores)
asymptotic_n <- 2048*900*2*3
(asymptotic_n%%10)==0
# maximum order of kernel
morder <- 6
#large sample size (asymptotic bias)
largesize<-2048*900*2
#generate quasirandom numbers based on the Sobol sequence
quasiunisobol_asymptotic<-sobol(n=asymptotic_n, dim = morder, init = TRUE, scrambling = 0, seed = NULL, normal = FALSE,
mixed = FALSE, method = "C", start = 1)
quasiuni_asymptotic<-rbind(quasiunisobol_asymptotic)
quasiunisobol_asymptotic<-c()
quasiuni_sorted2_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:2], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted3_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:3], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted4_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:4], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted5_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:5], descend = FALSE, stable = FALSE, parallel = TRUE))
quasiuni_sorted6_asymptotic <- na.omit(rowSort(quasiuni_asymptotic[,1:6], descend = FALSE, stable = FALSE, parallel = TRUE))
# Forever...
quasiuni_asymptotic<-(quasiuni_asymptotic[,1])
quasiuni_asymptotic<-quasiuni_asymptotic[1:largesize]
orderlist1_AB2_asymptotic<-createorderlist(quni1=quasiuni_sorted2_asymptotic,size=largesize,interval=8,dimension=2)
orderlist1_AB2_asymptotic<-orderlist1_AB2_asymptotic[1:largesize,]
orderlist1_AB3_asymptotic<-createorderlist(quni1=quasiuni_sorted3_asymptotic,size=largesize,interval=8,dimension=3)
orderlist1_AB3_asymptotic<-orderlist1_AB3_asymptotic[1:largesize,]
orderlist1_AB4_asymptotic<-createorderlist(quni1=quasiuni_sorted4_asymptotic,size=largesize,interval=8,dimension=4)
orderlist1_AB4_asymptotic<-orderlist1_AB4_asymptotic[1:largesize,]
orderlist1_AB5_asymptotic<-createorderlist(quni1=quasiuni_sorted5_asymptotic,size=largesize,interval=8,dimension=5)
orderlist1_AB5_asymptotic<-orderlist1_AB5_asymptotic[1:largesize,]
orderlist1_AB6_asymptotic<-createorderlist(quni1=quasiuni_sorted6_asymptotic,size=largesize,interval=8,dimension=6)
orderlist1_AB6_asymptotic<-orderlist1_AB6_asymptotic[1:largesize,]
quasiuni_sorted2_asymptotic<-c()
quasiuni_sorted3_asymptotic<-c()
quasiuni_sorted4_asymptotic<-c()
quasiuni_sorted5_asymptotic<-c()
quasiuni_sorted6_asymptotic<-c()
#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. Coorperation is also welcomed.
#Weibull
kurtWeibull<- read.csv(("kurtWeibull_31150.csv"))
allkurtWeibull<-unlist(kurtWeibull)
simulatedbatchWeibull_asymptoticbias<-foreach(batchnumber = (1:length(allkurtWeibull)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
library(rootSolve)
a=allkurtWeibull[batchnumber]
x<-c(dsWeibull(uni=quasiuni_asymptotic, shape=a/1, scale = 1))
targetm<-gamma(1+1/(a/1))
targetvar<-(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2)
targettm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^3)*(gamma(1+3/(a/1))-3*(gamma(1+1/(a/1)))*((gamma(1+2/(a/1))))+2*((gamma(1+1/(a/1)))^3))/((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(3))
targetfm<-((sqrt(gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^4)*(gamma(1+4/(a/1))-4*(gamma(1+3/(a/1)))*((gamma(1+1/(a/1))))+6*(gamma(1+2/(a/1)))*((gamma(1+1/(a/1)))^2)-3*((gamma(1+1/(a/1)))^4))/(((gamma(1+2/(a/1))-(gamma(((1+1/(a/1)))))^2))^(2))
kurtx<-targetfm/(targetvar^(4/2))
kurtx<-c(kurtx=kurtx)
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx)
SMWM9<-SWA9(x=sortedx,interval=9,batch="auto",sorted = TRUE)
midhinge1<-midhinge(x=sortedx,sorted = TRUE)
SWA81<-SWA8(x=sortedx,interval=8,batch="auto",sorted = TRUE)
SWAHlmean1<-SWAHLmean(x=sortedx,orderlist1_sorted2=orderlist1_AB2_asymptotic,orderlist1_sorted3=orderlist1_AB3_asymptotic,orderlist1_sorted4=orderlist1_AB4_asymptotic,orderlist1_sorted5=orderlist1_AB5_asymptotic,orderlist1_sorted6=orderlist1_AB6_asymptotic,batch="auto")
SWA22<-SWA(x = sortedx, percentage =1 - (1 - 1/2)^0.5, batch = "auto", sorted = TRUE, rand = TRUE)
rqm1<-rqm(x=sortedx,sorted = TRUE)
momentsx<-unbiasedmoments(x=sortedx)
sortedx<-c()
allrawmoBias<-c(
firstbias=abs(c(Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1)-targetm)/(sqrt(targetvar))
)
all1<-(c(kurtx,Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1,targetall,momentsx,allrawmoBias))
}
write.csv(simulatedbatchWeibull_asymptoticbias,paste("asymptotic_Weibull_SRM_Process",largesize,".csv", sep = ","), row.names = FALSE)
#gamma
kurtgamma<- read.csv(("kurtgamma_31150.csv"))
allkurtgamma<-unlist(kurtgamma)
simulatedbatchgamma_asymptoticbias<-foreach(batchnumber = (1:length(allkurtgamma)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
library(rootSolve)
a=allkurtgamma[batchnumber]
x<-c(dsgamma(uni=quasiuni_asymptotic, shape=a, rate = 1))
targetm<-a
targetvar<-(a)
targettm<-((sqrt(a))^3)*2/sqrt(a)
targetfm<-((sqrt(a))^4)*((6/(a))+3)
kurtx<-targetfm/(targetvar^(4/2))
kurtx<-c(kurtx=kurtx)
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx)
SMWM9<-SWA9(x=sortedx,interval=9,batch="auto",sorted = TRUE)
midhinge1<-midhinge(x=sortedx,sorted = TRUE)
SWA81<-SWA8(x=sortedx,interval=8,batch="auto",sorted = TRUE)
SWAHlmean1<-SWAHLmean(x=sortedx,orderlist1_sorted2=orderlist1_AB2_asymptotic,orderlist1_sorted3=orderlist1_AB3_asymptotic,orderlist1_sorted4=orderlist1_AB4_asymptotic,orderlist1_sorted5=orderlist1_AB5_asymptotic,orderlist1_sorted6=orderlist1_AB6_asymptotic,batch="auto")
SWA22<-SWA(x = sortedx, percentage =1 - (1 - 1/2)^0.5, batch = "auto", sorted = TRUE, rand = TRUE)
rqm1<-rqm(x=sortedx,sorted = TRUE)
momentsx<-unbiasedmoments(x=sortedx)
sortedx<-c()
allrawmoBias<-c(
firstbias=abs(c(Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1)-targetm)/(sqrt(targetvar))
)
all1<-(c(kurtx,Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1,targetall,momentsx,allrawmoBias))
}
write.csv(simulatedbatchgamma_asymptoticbias,paste("asymptotic_gamma_SRM_Process",largesize,".csv", sep = ","), row.names = FALSE)
#Pareto
kurtPareto<- read.csv(("kurtPareto_91210.csv"))
allkurtPareto<-unlist(kurtPareto)
simulatedbatchPareto_asymptoticbias<-foreach(batchnumber = (1:length(allkurtPareto)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
library(rootSolve)
a=allkurtPareto[batchnumber]
x<-c(dsPareto(uni=quasiuni_asymptotic, shape=a, scale = 1))
targetm<-a/(a-1)
targetvar<-(((a))*(1)/((-2+(a))*((-1+(a))^2)))
targettm<-((((a)+1)*(2)*(sqrt(a-2)))/((-3+(a))*(((a))^(1/2))))*(((sqrt(((a))*(1)/((-2+(a))*((-1+(a))^2))))^3))
targetfm<-(3+(6*((a)^3+(a)^2-6*(a)-2)/(((a))*((-3+(a)))*((-4+(a))))))*((sqrt(((a))*(1)/((-2+(a))*((-1+(a))^2))))^4)
kurtx<-targetfm/(targetvar^(4/2))
kurtx<-c(kurtx=kurtx)
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx)
SMWM9<-SWA9(x=sortedx,interval=9,batch="auto",sorted = TRUE)
midhinge1<-midhinge(x=sortedx,sorted = TRUE)
SWA81<-SWA8(x=sortedx,interval=8,batch="auto",sorted = TRUE)
SWAHlmean1<-SWAHLmean(x=sortedx,orderlist1_sorted2=orderlist1_AB2_asymptotic,orderlist1_sorted3=orderlist1_AB3_asymptotic,orderlist1_sorted4=orderlist1_AB4_asymptotic,orderlist1_sorted5=orderlist1_AB5_asymptotic,orderlist1_sorted6=orderlist1_AB6_asymptotic,batch="auto")
SWA22<-SWA(x = sortedx, percentage =1 - (1 - 1/2)^0.5, batch = "auto", sorted = TRUE, rand = TRUE)
rqm1<-rqm(x=sortedx,sorted = TRUE)
momentsx<-unbiasedmoments(x=sortedx)
sortedx<-c()
allrawmoBias<-c(
firstbias=abs(c(Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1)-targetm)/(sqrt(targetvar))
)
all1<-(c(kurtx,Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1,targetall,momentsx,allrawmoBias))
}
write.csv(simulatedbatchPareto_asymptoticbias,paste("asymptotic_Pareto_SRM_Process",largesize,".csv", sep = ","), row.names = FALSE)
#lognorm
kurtlognorm<- read.csv(("kurtlognorm_31150.csv"))
allkurtlognorm<-unlist(kurtlognorm)
simulatedbatchlognorm_asymptoticbias<-foreach(batchnumber = (1:length(allkurtlognorm)), .combine = 'rbind') %dopar% {
library(Rfast)
library(matrixStats)
library(REDSReview)
library(rootSolve)
a=allkurtlognorm[batchnumber]
x<-c(dslnorm(uni=quasiuni_asymptotic, meanlog =0, sdlog = a/1))
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))
kurtx<-c(kurtx=kurtx)
sortedx<-Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
targetall<-c(targetm=targetm,targetvar=targetvar,targettm=targettm,targetfm=targetfm)
x<-c()
Huberx<-Huber_estimator(x=sortedx)
SMWM9<-SWA9(x=sortedx,interval=9,batch="auto",sorted = TRUE)
midhinge1<-midhinge(x=sortedx,sorted = TRUE)
SWA81<-SWA8(x=sortedx,interval=8,batch="auto",sorted = TRUE)
SWAHlmean1<-SWAHLmean(x=sortedx,orderlist1_sorted2=orderlist1_AB2_asymptotic,orderlist1_sorted3=orderlist1_AB3_asymptotic,orderlist1_sorted4=orderlist1_AB4_asymptotic,orderlist1_sorted5=orderlist1_AB5_asymptotic,orderlist1_sorted6=orderlist1_AB6_asymptotic,batch="auto")
SWA22<-SWA(x = sortedx, percentage =1 - (1 - 1/2)^0.5, batch = "auto", sorted = TRUE, rand = TRUE)
rqm1<-rqm(x=sortedx,sorted = TRUE)
momentsx<-unbiasedmoments(x=sortedx)
sortedx<-c()
allrawmoBias<-c(
firstbias=abs(c(Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1)-targetm)/(sqrt(targetvar))
)
all1<-(c(kurtx,Huberx,SMWM9,midhinge1,SWA81,SWAHlmean1,SWAHL=SWA22,rqm1,targetall,momentsx,allrawmoBias))
}
write.csv(simulatedbatchlognorm_asymptoticbias,paste("asymptotic_lognorm_SRM_Process",largesize,".csv", sep = ","), row.names = FALSE)
registerDoSEQ()