vignettes/NNSvignette_Sampling.R
In OVVO-Financial/NNS: Nonlinear Nonparametric Statistics
## ----setup, include=FALSE, message=FALSE--------------------------------------
knitr::opts_chunk$set(echo = TRUE)
library(NNS)
library(data.table)
data.table::setDTthreads(2L)
options(mc.cores = 1)
Sys.setenv("OMP_THREAD_LIMIT" = 2)
## ----setup2, message=FALSE, warning = FALSE-----------------------------------
library(NNS)
library(data.table)
require(knitr)
require(rgl)
## -----------------------------------------------------------------------------
set.seed(123); x = rnorm(100)
ecdf(x)
P = ecdf(x)
P(0); P(1)
## ----message=FALSE------------------------------------------------------------
LPM.ratio(degree = 0, target = 0, variable = x); LPM.ratio(degree = 0, target = 1, variable = x)
## ----fig.align='center', fig.width=6, fig.height=6, echo = FALSE--------------
LPM.CDF = LPM.ratio(degree = 0, target = sort(x), variable = x)
plot(ecdf(x))
points(sort(x), LPM.CDF, col='red')
legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA, bty='n')
## ----fig.align='center', fig.height=8, fig.width=8, echo=FALSE, warning=FALSE, message = FALSE, eval=FALSE----
# zzz= rnorm(length(x), mean = 0, sd = 1)
# norm_approx = pnorm(sort(zzz), mean=0, sd=1) #pnorm(sort(x),mean=-mean(x),sd=sd(x))
#
# plot(ecdf(x), main = "eCDF via LPM.ratio()", lwd = 4)
#
#
# # Altering shape of distribution with LPM degree
# for(i in c(0, 0.25, .5, 1, 2)){
# idx <- which(i == c(0, 0.25, .5, 1, 2))
# lines(sort(x), LPM.ratio(i, sort(x),x), col = rainbow(5, alpha = 1)[idx], lty = 1, lwd = 3)
# }
#
# lines(sort(zzz), norm_approx ,col='black', lty = 3, lwd = 2)
#
#
# legend("topleft",c("LPM.ratio(degree = 0)","LPM.ratio(degree = 0.25)","LPM.ratio(degree = 0.5)","LPM.ratio(degree = 1)","LPM.ratio(degree = 2)", "N(0,1) approximation"),
# col = c(rainbow(5)[1:5], "black"), lwd = 3, lty = c(rep(1, 5), 3))
## ----fig.align='center', echo=FALSE, fig.width=10, fig.height=8, message=FALSE, warning=FALSE, eval=FALSE----
# layout(matrix(c(1, 1, 1,1,1,
# 2, 3, 4,5,6,
# 2, 3, 4,5,6), nrow=5, byrow=FALSE),widths = c(2,rep(1,5)))
#
#
# plot(ecdf(x), main = "eCDF via LPM.ratio()", lwd = 4)
#
#
# # Altering shape of distribution with LPM degree
# for(i in c(0, 0.25, .5, 1, 2)){
# idx <- which(i == c(0, 0.25, .5, 1, 2))
# lines(sort(x), LPM.ratio(i, sort(x),x), col = rainbow(5, alpha = 1)[idx], lty = 1, lwd = 3)
# }
#
# lines(sort(zzz), norm_approx ,col='black', lty = 3, lwd = 2)
#
#
# legend("topleft",c("LPM.ratio(degree = 0)","LPM.ratio(degree = 0.25)","LPM.ratio(degree = 0.5)","LPM.ratio(degree = 1)","LPM.ratio(degree = 2)", "N(0,1) approximation"),
# col = c(rainbow(5)[1:5], "black"), lwd = 3, lty = c(rep(1, 5), 3))
#
#
#
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
#
# plot(y$breaks,
# c(y$counts,0), type = "s",
# col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 0)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), add = TRUE, col = rainbow(5, alpha = .5)[1], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), border = NA, plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 0.25)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), .25, x), border = rainbow(5)[2], add = TRUE, col = rainbow(5, alpha = .5)[2], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 0.5)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), .5, x), border = rainbow(5)[3], add = TRUE, col = rainbow(5, alpha = .5)[3], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 1)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), 1, x), border = rainbow(5)[4], add = TRUE, col = rainbow(5, alpha = .5)[4], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 2)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), 2, x), border = rainbow(5)[5], add = TRUE, col = rainbow(5, alpha = .5)[5], breaks = 15)
## ----eval=FALSE---------------------------------------------------------------
# degree.0.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 0, x = x)
# degree.0.25.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 0.25, x = x)
# degree.0.5.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 0.5, x = x)
# degree.1.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 1, x = x)
# degree.2.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 2, x = x)
#
# head(data.table::data.table(cbind("original x" = sort(x), degree.0.samples,
# degree.0.25.samples,
# degree.0.5.samples,
# degree.1.samples,
# degree.2.samples)), 10)
#
# original x degree.0.samples degree.0.25.samples degree.0.5.samples
# 1: -2.309169 -2.309169 -2.309097 -2.3090915
# 2: -1.966617 -1.966617 -1.941190 -1.6935509
# 3: -1.686693 -1.686693 -1.599486 -1.4541494
# 4: -1.548753 -1.548753 -1.382553 -1.2462731
# 5: -1.265396 -1.265396 -1.250823 -1.1453748
# 6: -1.265061 -1.265061 -1.176436 -1.0745440
# 7: -1.220718 -1.220718 -1.119655 -1.0252742
# 8: -1.138137 -1.138137 -1.067793 -0.9868693
# 9: -1.123109 -1.123109 -1.026429 -0.9322105
# 10: -1.071791 -1.071791 -1.014276 -0.8710942
# degree.1.samples degree.2.samples
# 1: -2.3091021 -2.3091170
# 2: -1.4744653 -1.1614908
# 3: -1.2159961 -0.9709972
# 4: -1.0823023 -0.8610192
# 5: -0.9968028 -0.7810300
# 6: -0.9290505 -0.7169770
# 7: -0.8666886 -0.6631888
# 8: -0.8090433 -0.6170691
# 9: -0.7556644 -0.5765608
# 10: -0.7069835 -0.5403318
## ----fig.align='center', fig.width=8, fig.height=8, eval=FALSE----------------
# boots = NNS.MC(x, reps = 1, lower_rho = -1, upper_rho = 1, by = .5)$replicates
# reps = do.call(cbind, boots)
#
# plot(x, type = "l", lwd = 3, ylim = c(min(reps), max(reps)))
# matplot(reps, type = "l", col = rainbow(length(boots)), add = TRUE)
## ----eval = FALSE-------------------------------------------------------------
# sapply(boots, function(r) cor(r, x, method = "spearman"))
#
# rho = 1 rho = 0.5 rho = -0.5 rho = -1
# 1.0000000 0.4988059 -0.4995740 -0.9982358
## ----multisim, eval=FALSE-----------------------------------------------------
# set.seed(123)
# x <- rnorm(1000); y <- rnorm(1000); z <- rnorm(1000)
#
# # Add variable x to original data to avoid total independence (example only)
# original.data <- cbind(x, y, z, x)
#
# # Determine dependence structure
# dep.structure <- apply(original.data, 2, function(x) LPM.ratio(degree = 1, target = x, variable = x))
#
# # Generate new data with different mean, sd and length (or distribution type)
# new.data <- sapply(1:ncol(original.data), function(x) rnorm(nrow(original.data)*2, mean = 10, sd = 20))
#
# # Apply dependence structure to new data
# new.dep.data <- sapply(1:ncol(original.data), function(x) LPM.VaR(percentile = dep.structure[,x], degree = 1, x = new.data[,x]))
## ----comparison, warning=FALSE, eval=FALSE------------------------------------
# NNS.copula(original.data)
# NNS.copula(new.dep.data)
#
# [1] 0.4379469
# [1] 0.4390599
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
# head(new.dep.data)
#
# x y z x
# [1,] -0.56047565 -0.99579872 -0.5116037 -0.56047565
# [2,] -0.23017749 -1.03995504 0.2369379 -0.23017749
# [3,] 1.55870831 -0.01798024 -0.5415892 1.55870831
# [4,] 0.07050839 -0.13217513 1.2192276 0.07050839
# [5,] 0.12928774 -2.54934277 0.1741359 0.12928774
# [6,] 1.71506499 1.04057346 -0.6152683 1.71506499
# [,1] [,2] [,3] [,4]
# [1,] -2.028109 -10.498044 -0.2090467 -1.682949
# [2,] 4.608303 -11.390485 15.6213689 4.852534
# [3,] 39.478741 8.836581 -0.8508203 40.585505
# [4,] 10.683731 6.609255 36.0328589 10.877677
# [5,] 11.866922 -47.955235 14.3111350 12.064633
# [6,] 42.665726 29.639640 -2.4141874 43.797025
## ----eval=FALSE---------------------------------------------------------------
# # Apply bootstrap to each variable
# new.boot.dep.data = apply(original.data, 2, function(r) NNS.meboot(r, reps = 1, rho = .95))
#
# # Reformat into vectors
# boot.ensemble.vectors = lapply(new.boot.dep.data, function(z) unlist(z["ensemble",]))
#
# # Create matrix from vectors
# new.boot.dep.matrix = do.call(cbind, boot.ensemble.vectors)
## ----eval=FALSE---------------------------------------------------------------
# for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
#
# [1] 0.9453275
# [1] 0.9523726
# [1] 0.9498499
# [1] 0.9524516
## ----eval=FALSE---------------------------------------------------------------
# NNS.copula(original.data)
# NNS.copula(new.boot.dep.matrix)
#
# [1] 0.4379469
# [1] 0.4302545
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
# head(new.boot.dep.matrix)
#
# x y z x
# [1,] -0.56047565 -0.99579872 -0.5116037 -0.56047565
# [2,] -0.23017749 -1.03995504 0.2369379 -0.23017749
# [3,] 1.55870831 -0.01798024 -0.5415892 1.55870831
# [4,] 0.07050839 -0.13217513 1.2192276 0.07050839
# [5,] 0.12928774 -2.54934277 0.1741359 0.12928774
# [6,] 1.71506499 1.04057346 -0.6152683 1.71506499
# x y z x
# ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
# ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
# ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
# ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
# ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
# ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
## ----threads, echo = FALSE----------------------------------------------------
Sys.setenv("OMP_THREAD_LIMIT" = "")
OVVO-Financial/NNS documentation built on April 22, 2024, 10:26 p.m.
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## ----setup, include=FALSE, message=FALSE--------------------------------------
knitr::opts_chunk$set(echo = TRUE)
library(NNS)
library(data.table)
data.table::setDTthreads(2L)
options(mc.cores = 1)
Sys.setenv("OMP_THREAD_LIMIT" = 2)
## ----setup2, message=FALSE, warning = FALSE-----------------------------------
library(NNS)
library(data.table)
require(knitr)
require(rgl)
## -----------------------------------------------------------------------------
set.seed(123); x = rnorm(100)
ecdf(x)
P = ecdf(x)
P(0); P(1)
## ----message=FALSE------------------------------------------------------------
LPM.ratio(degree = 0, target = 0, variable = x); LPM.ratio(degree = 0, target = 1, variable = x)
## ----fig.align='center', fig.width=6, fig.height=6, echo = FALSE--------------
LPM.CDF = LPM.ratio(degree = 0, target = sort(x), variable = x)
plot(ecdf(x))
points(sort(x), LPM.CDF, col='red')
legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA, bty='n')
## ----fig.align='center', fig.height=8, fig.width=8, echo=FALSE, warning=FALSE, message = FALSE, eval=FALSE----
# zzz= rnorm(length(x), mean = 0, sd = 1)
# norm_approx = pnorm(sort(zzz), mean=0, sd=1) #pnorm(sort(x),mean=-mean(x),sd=sd(x))
#
# plot(ecdf(x), main = "eCDF via LPM.ratio()", lwd = 4)
#
#
# # Altering shape of distribution with LPM degree
# for(i in c(0, 0.25, .5, 1, 2)){
# idx <- which(i == c(0, 0.25, .5, 1, 2))
# lines(sort(x), LPM.ratio(i, sort(x),x), col = rainbow(5, alpha = 1)[idx], lty = 1, lwd = 3)
# }
#
# lines(sort(zzz), norm_approx ,col='black', lty = 3, lwd = 2)
#
#
# legend("topleft",c("LPM.ratio(degree = 0)","LPM.ratio(degree = 0.25)","LPM.ratio(degree = 0.5)","LPM.ratio(degree = 1)","LPM.ratio(degree = 2)", "N(0,1) approximation"),
# col = c(rainbow(5)[1:5], "black"), lwd = 3, lty = c(rep(1, 5), 3))
## ----fig.align='center', echo=FALSE, fig.width=10, fig.height=8, message=FALSE, warning=FALSE, eval=FALSE----
# layout(matrix(c(1, 1, 1,1,1,
# 2, 3, 4,5,6,
# 2, 3, 4,5,6), nrow=5, byrow=FALSE),widths = c(2,rep(1,5)))
#
#
# plot(ecdf(x), main = "eCDF via LPM.ratio()", lwd = 4)
#
#
# # Altering shape of distribution with LPM degree
# for(i in c(0, 0.25, .5, 1, 2)){
# idx <- which(i == c(0, 0.25, .5, 1, 2))
# lines(sort(x), LPM.ratio(i, sort(x),x), col = rainbow(5, alpha = 1)[idx], lty = 1, lwd = 3)
# }
#
# lines(sort(zzz), norm_approx ,col='black', lty = 3, lwd = 2)
#
#
# legend("topleft",c("LPM.ratio(degree = 0)","LPM.ratio(degree = 0.25)","LPM.ratio(degree = 0.5)","LPM.ratio(degree = 1)","LPM.ratio(degree = 2)", "N(0,1) approximation"),
# col = c(rainbow(5)[1:5], "black"), lwd = 3, lty = c(rep(1, 5), 3))
#
#
#
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
#
# plot(y$breaks,
# c(y$counts,0), type = "s",
# col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 0)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), add = TRUE, col = rainbow(5, alpha = .5)[1], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), border = NA, plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 0.25)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), .25, x), border = rainbow(5)[2], add = TRUE, col = rainbow(5, alpha = .5)[2], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 0.5)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), .5, x), border = rainbow(5)[3], add = TRUE, col = rainbow(5, alpha = .5)[3], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 1)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), 1, x), border = rainbow(5)[4], add = TRUE, col = rainbow(5, alpha = .5)[4], breaks = 15)
#
# y = hist(LPM.VaR(seq(0,1,length.out = 100), 0, x), plot = FALSE, breaks = 15)
# plot(y$breaks,
# c(y$counts,0)
# ,type="s",col="black",lwd = 3, ylim = c(0,50), main = "Inverse CDF via LPM.VaR(degree 2)", breaks = 15, xlab = "x", ylab = "freq")
# hist(LPM.VaR(seq(0,1,length.out = 100), 2, x), border = rainbow(5)[5], add = TRUE, col = rainbow(5, alpha = .5)[5], breaks = 15)
## ----eval=FALSE---------------------------------------------------------------
# degree.0.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 0, x = x)
# degree.0.25.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 0.25, x = x)
# degree.0.5.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 0.5, x = x)
# degree.1.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 1, x = x)
# degree.2.samples = LPM.VaR(percentile = seq(0, 1, length.out = 100), degree = 2, x = x)
#
# head(data.table::data.table(cbind("original x" = sort(x), degree.0.samples,
# degree.0.25.samples,
# degree.0.5.samples,
# degree.1.samples,
# degree.2.samples)), 10)
#
# original x degree.0.samples degree.0.25.samples degree.0.5.samples
# 1: -2.309169 -2.309169 -2.309097 -2.3090915
# 2: -1.966617 -1.966617 -1.941190 -1.6935509
# 3: -1.686693 -1.686693 -1.599486 -1.4541494
# 4: -1.548753 -1.548753 -1.382553 -1.2462731
# 5: -1.265396 -1.265396 -1.250823 -1.1453748
# 6: -1.265061 -1.265061 -1.176436 -1.0745440
# 7: -1.220718 -1.220718 -1.119655 -1.0252742
# 8: -1.138137 -1.138137 -1.067793 -0.9868693
# 9: -1.123109 -1.123109 -1.026429 -0.9322105
# 10: -1.071791 -1.071791 -1.014276 -0.8710942
# degree.1.samples degree.2.samples
# 1: -2.3091021 -2.3091170
# 2: -1.4744653 -1.1614908
# 3: -1.2159961 -0.9709972
# 4: -1.0823023 -0.8610192
# 5: -0.9968028 -0.7810300
# 6: -0.9290505 -0.7169770
# 7: -0.8666886 -0.6631888
# 8: -0.8090433 -0.6170691
# 9: -0.7556644 -0.5765608
# 10: -0.7069835 -0.5403318
## ----fig.align='center', fig.width=8, fig.height=8, eval=FALSE----------------
# boots = NNS.MC(x, reps = 1, lower_rho = -1, upper_rho = 1, by = .5)$replicates
# reps = do.call(cbind, boots)
#
# plot(x, type = "l", lwd = 3, ylim = c(min(reps), max(reps)))
# matplot(reps, type = "l", col = rainbow(length(boots)), add = TRUE)
## ----eval = FALSE-------------------------------------------------------------
# sapply(boots, function(r) cor(r, x, method = "spearman"))
#
# rho = 1 rho = 0.5 rho = -0.5 rho = -1
# 1.0000000 0.4988059 -0.4995740 -0.9982358
## ----multisim, eval=FALSE-----------------------------------------------------
# set.seed(123)
# x <- rnorm(1000); y <- rnorm(1000); z <- rnorm(1000)
#
# # Add variable x to original data to avoid total independence (example only)
# original.data <- cbind(x, y, z, x)
#
# # Determine dependence structure
# dep.structure <- apply(original.data, 2, function(x) LPM.ratio(degree = 1, target = x, variable = x))
#
# # Generate new data with different mean, sd and length (or distribution type)
# new.data <- sapply(1:ncol(original.data), function(x) rnorm(nrow(original.data)*2, mean = 10, sd = 20))
#
# # Apply dependence structure to new data
# new.dep.data <- sapply(1:ncol(original.data), function(x) LPM.VaR(percentile = dep.structure[,x], degree = 1, x = new.data[,x]))
## ----comparison, warning=FALSE, eval=FALSE------------------------------------
# NNS.copula(original.data)
# NNS.copula(new.dep.data)
#
# [1] 0.4379469
# [1] 0.4390599
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
# head(new.dep.data)
#
# x y z x
# [1,] -0.56047565 -0.99579872 -0.5116037 -0.56047565
# [2,] -0.23017749 -1.03995504 0.2369379 -0.23017749
# [3,] 1.55870831 -0.01798024 -0.5415892 1.55870831
# [4,] 0.07050839 -0.13217513 1.2192276 0.07050839
# [5,] 0.12928774 -2.54934277 0.1741359 0.12928774
# [6,] 1.71506499 1.04057346 -0.6152683 1.71506499
# [,1] [,2] [,3] [,4]
# [1,] -2.028109 -10.498044 -0.2090467 -1.682949
# [2,] 4.608303 -11.390485 15.6213689 4.852534
# [3,] 39.478741 8.836581 -0.8508203 40.585505
# [4,] 10.683731 6.609255 36.0328589 10.877677
# [5,] 11.866922 -47.955235 14.3111350 12.064633
# [6,] 42.665726 29.639640 -2.4141874 43.797025
## ----eval=FALSE---------------------------------------------------------------
# # Apply bootstrap to each variable
# new.boot.dep.data = apply(original.data, 2, function(r) NNS.meboot(r, reps = 1, rho = .95))
#
# # Reformat into vectors
# boot.ensemble.vectors = lapply(new.boot.dep.data, function(z) unlist(z["ensemble",]))
#
# # Create matrix from vectors
# new.boot.dep.matrix = do.call(cbind, boot.ensemble.vectors)
## ----eval=FALSE---------------------------------------------------------------
# for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
#
# [1] 0.9453275
# [1] 0.9523726
# [1] 0.9498499
# [1] 0.9524516
## ----eval=FALSE---------------------------------------------------------------
# NNS.copula(original.data)
# NNS.copula(new.boot.dep.matrix)
#
# [1] 0.4379469
# [1] 0.4302545
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
# head(new.boot.dep.matrix)
#
# x y z x
# [1,] -0.56047565 -0.99579872 -0.5116037 -0.56047565
# [2,] -0.23017749 -1.03995504 0.2369379 -0.23017749
# [3,] 1.55870831 -0.01798024 -0.5415892 1.55870831
# [4,] 0.07050839 -0.13217513 1.2192276 0.07050839
# [5,] 0.12928774 -2.54934277 0.1741359 0.12928774
# [6,] 1.71506499 1.04057346 -0.6152683 1.71506499
# x y z x
# ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
# ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
# ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
# ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
# ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
# ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
## ----threads, echo = FALSE----------------------------------------------------
Sys.setenv("OMP_THREAD_LIMIT" = "")
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