Nothing
R/plugin_dist.R
In binnednp: Nonparametric Estimation for Interval-Grouped Data
#' Plug-in bandwidth selector for kernel distribution estimation and binned data.
#'
#' @param n Positive integer. Size of the complete sample.
#' @param y Vector. Observed values. They define the extremes of the sequence of intervals in which data is binned.
#' @param w Vector. Proportion of observations within each interval.
#' @param ni Vector. Number of observations within each interval.
#' @param gplugin Positive real number. Pilot bandwidth. If missing, rule-of-thumb bandwidth is considered.
#' @param confband Logical. If TRUE, bootstrap confidence bands for the distribution are constructed. Defaults to FALSE.
#' @param alpha Significance level for the bootstrap confidence bands. Defaults to 0.05.
#' @param B Number of bootstrap resamples. Defaults to 1000.
#' @param type Character. If \code{type} = "N", normality is assumed at the last step when calculating the plug-in bandwidth. If \code{type} = "A", parameter at last step is estimated nonparametrically using \code{gplugin} as bandwidth. Otherwise, the unknown parameter is estimated fitting a normal mixture. Defaults to \code{type} = "N".
#' @param plot Logical. If TRUE, results are plotted. Defaults to TRUE.
#' @param print Logical. If TRUE, script current status is printed. Defaults to TRUE.
#' @param model Character. Name of the parametric family of distributions to be fitted for the grouped sample. Parameters are estimated by maximum likelihood.
#' @param parallel Logical. If TRUE, confidence bands are estimated using parallel computing with sockets.
#' @param pars Environment. Needed for the well functioning of the script. DO NOT modify this argument.
#'
#' @return A list with components
#' \item{h}{Plug-in bandwidth.}
#' \item{Fh}{Function. Kernel distribution estimator with bandwidth \code{h}.}
#' \item{confband}{(Optional) Bootstrap confidence bands for the distribution function.}
#'
#' @examples
#' set.seed(1)
#' n <- 200 #complete sample size
#' k <- 30 #number of intervals
#' x <- rnorm(n,6,1) #complete sample
#' y <- seq(min(x)-0.2,max(x)+0.2,len=k+1) #intervals
#' w <- c(sapply(2:k,function(i)sum( x<y[i]&x>=y[i-1] )), sum(x<=y[k+1]&x>=y[k]) )/n #proportions
#' bw.dist.binned(n,y,w,plot=FALSE)
#'
#' @references
#' \insertRef{TesisMiguel2015}{binnednp}
#'
#' \insertRef{Phalaris2016}{binnednp}
#'
#' @useDynLib binnednp
#' @importFrom Rcpp sourceCpp
#'
#' @export
bw.dist.binned <- function(n,y,w,ni,gplugin,type="N",confband=F,B=1000,alpha=0.05,plot=TRUE,print=TRUE,model,parallel=FALSE,pars=new.env()){
main <- !exists("k", where = pars, inherits = FALSE)
if(main==TRUE){
t <- y[-length(y)]+diff(y)/2
k <- length(t)
if(missing(w)){
if(!missing(ni)){
if(missing(n)) n <- sum(ni)
w <- ni/n
} else {
stop("Arguments w or ni must be provided.")
}
}
if(anyDuplicated(y) != 0){
dup <- which(duplicated(y))
comby <- y[-dup]
lcy <- length(comby)
combw <- numeric(lcy-1)
for(i in 2:lcy){
combw[i-1] <- sum(w[which(y==comby[i])-1])
}
combt <- comby[-lcy]+diff(comby)/2
t <- combt
y <- comby
w <- combw
k <- lcy-1
}
K <- function(x) stats::dnorm(x)
pK <- Vectorize(function(x) stats::pnorm(x))
C0 <- 2*stats::integrate(function(x)x*K(x)*pK(x),-Inf,Inf)$value
l <- mean(diff(y))
K2 <- function(x) (x^2-1)*stats::dnorm(x)
K4 <- function(x) ((x^2-3)*(x^2-1)-2*x^2)*stats::dnorm(x)
K6_0 <- kedd::kernel.fun(0,deriv.order=6,kernel="gaussian")$kx
K8_0 <- kedd::kernel.fun(0,deriv.order=8,kernel="gaussian")$kx
L1 <- function(w,h) -sum( sapply( 1:k,function(i) sum(K2((t[i]-t)/h)*w[i]*w) ) )/h^3 # Af1=-psi2
L2 <- function(w,h) sum( sapply( 1:k,function(i) sum(K4((t[i]-t)/h)*w[i]*w) ) )/h^5 # Af2=psi4
L3 <- function(w,h) -sum( sapply( 1:k,function(i) sum(kedd::kernel.fun((t[i]-t)/h,deriv.order=6,kernel="gaussian")$kx*w[i]*w) ) )/h^7
L4 <- function(w,h) sum( sapply( 1:k,function(i) sum(kedd::kernel.fun((t[i]-t)/h,deriv.order=8,kernel="gaussian")$kx*w[i]*w) ) )/h^9
L5 <- function(w,h) -sum( sapply( 1:k,function(i) sum(kedd::kernel.fun((t[i]-t)/h,deriv.order=10,kernel="gaussian")$kx*w[i]*w) ) )/h^11
} else {
t <- pars$t
k <- pars$k
y <- pars$y
K <- pars$K
pK <- pars$pK
C0 <- pars$C0
l <- pars$l
K2 <- pars$K2
K4 <- pars$K4
K6_0 <- pars$K6_0
K8_0 <- pars$K8_0
L1 <- pars$L1
L2 <- pars$L2
L3 <- pars$L3
L4 <- pars$L4
L5 <- pars$L5
}
mu_hat <- sum(w*t)
sigma_hat <- sqrt( sum(w*(t-mu_hat)^2) )
if(type == "N" || type == "A"){
if(missing(gplugin)) gplugin <- 1.59*sigma_hat*n^(-1/3)
if(type == "A"){
f_gplugin <- Vectorize(function(x)1/gplugin*sum(w*K((x-t)/gplugin)))
llim <- mu_hat-3*sigma_hat
rlim <- mu_hat+3*sigma_hat
Af <- stats::integrate(function(x)f_gplugin(x)^2,llim,rlim)$value
if(!exists("Af")) Af <- stats::integrate(function(x)f_gplugin(x)^2,y[1],y[k+1])$value
psi10 <- -L5(w,gplugin)
} else {
Af <- 1/(2*sqrt(pi)*sigma_hat)
psi10 <- -30240/((2*sigma_hat)^11*sqrt(pi))
}
eta8 <- (-2*K8_0*Af*l/psi10)^(1/11)
psi8 <- L4(w,eta8)
eta6 <- (-2*K6_0*Af*l/psi8)^(1/9)
psi6 <- -L3(w,eta6)
eta4 <- (-2*K4(0)*Af*l/psi6)^(1/7)
psi4 <- L2(w,eta4)
eta2 <- (-2*K2(0)*Af*l/psi4)^(1/5)
Af1 <- L1(w,eta2)
} else {
clustering <- mclust::Mclust(rep(t,n*w),G=1:5,verbose=FALSE,modelNames="V")
mix_params <- clustering$parameters
mu_mixt <- mix_params$mean
sigma_mixt <- sqrt(mix_params$variance$sigmasq)
alfa_mixt <- mix_params$pro
normal_mixt <- nor1mix::norMix(mu=mu_mixt,sigma=sigma_mixt,w=alfa_mixt)
f1_mixt <- Vectorize( function(x) -sum(alfa_mixt*(x-mu_mixt)/sigma_mixt^3*stats::dnorm((x-mu_mixt)/sigma_mixt)) )
mixlim1 <- nor1mix::qnorMix(0.001,normal_mixt)
mixlim2 <- nor1mix::qnorMix(0.999,normal_mixt)
Af1 <- stats::integrate(function(x)f1_mixt(x)^2,mixlim1,mixlim2)$value
}
h_AMISE <- ( C0/(n*Af1) )^(1/3)
if(main == TRUE){
x <- NULL
Fh <- Vectorize( function(x)sum(w*stats::pnorm((x-t)/h_AMISE)) )
}
if(confband == T){
pars$t <- t
pars$k <- k
pars$y <- y
pars$K <- K
pars$pK <- pK
pars$C0 <- C0
pars$l <- l
pars$K2 <- K2
pars$K4 <- K4
pars$K6_0 <- K6_0
pars$K8_0 <- K8_0
pars$L1 <- L1
pars$L2 <- L2
pars$L3 <- L3
pars$L4 <- L4
pars$L5 <- L5
gplugin <- bw.dist.binned.boot(n,y,w,pilot.type=2,print=FALSE)$h
Fhy <- sapply(y, function(x)sum( w*stats::pnorm((x-t)/h_AMISE) ))
Fg <- Vectorize(function(x)sum( w*stats::pnorm((x-t)/gplugin) ))
Fgy <- Fg(y)
Dn <- matrix(0,nrow=length(y),ncol=B)
if(!parallel){
for(b in 1:B){
rx <- sort(sample(t,replace=T,size=n,prob=w)+gplugin*stats::rnorm(n))
wb <- calcw_cpp(rx,y)
h_AMISE_boot <- bw.dist.binned(n,y,wb,plot=FALSE,print=FALSE,type=type,pars=pars)
Fhby <- sapply(y,function(x)sum( wb*stats::pnorm( (x-t)/h_AMISE_boot ) ))
Dn[,b] <- Fhby
if(print == TRUE) cat("\rConstructing bootstrap confidence bands. Progress:",floor(100*b/B),"%")
}
} else {
parfun <- function(b){
rx <- sort(sample(t,replace=T,size=n,prob=w)+gplugin*stats::rnorm(n))
wb <- calcw_cpp(rx,y)
h_AMISE_boot <- bw.dist.binned(n,y,wb,plot=FALSE,print=FALSE,type=type,pars=pars)
Fhby <- sapply(y,function(x)sum( wb*stats::pnorm( (x-t)/h_AMISE_boot ) ))
return(Fhby)
}
ncores <- parallel::detectCores()
cl <- parallel::makeCluster(ncores)
parallel::clusterEvalQ(cl, library(binnednp))
parallel::clusterExport(cl, 'calcw_cpp')
paroutput <- parallel::parSapply(cl, 1:B, parfun)
Dn <- paroutput
parallel::stopCluster(cl)
}
alfa <- alpha/length(y)
count <- 0
maxcount <- 100
low.alpha <- alfa
high.alpha <- alpha
if(print == TRUE) cat("\n")
while(count < maxcount){
if(print == TRUE) cat("\rAdjusting significance level. Progress:",floor(100*(count+1)/maxcount),"%")
mean.alpha <- 0.5*(low.alpha+high.alpha)
q1 <- apply(Dn,1,function(i)stats::quantile(i,low.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-low.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
p_low.alpha <- sapply(1:B,function(b){
aux <- ifelse(Dn[,b] < banda1 && Dn[,b] > banda2,1,0)
return(aux)
})
p_low.alpha <- sum(p_low.alpha)/B
q1 <- apply(Dn,1,function(i)stats::quantile(i,high.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-high.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
p_high.alpha <- sapply(1:B,function(b){
aux <- ifelse(Dn[,b] < banda1 && Dn[,b] > banda2,1,0)
return(aux)
})
p_high.alpha <- sum(p_high.alpha)/B
q1 <- apply(Dn,1,function(i)stats::quantile(i,mean.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-mean.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
p_mean.alpha <- sapply(1:B,function(b){
aux <- ifelse(Dn[,b] < banda1 && Dn[,b] > banda2,1,0)
return(aux)
})
p_mean.alpha <- sum(p_mean.alpha)/B
if(p_mean.alpha >= 1-alpha){
low.alpha <- mean.alpha
} else {
high.alpha <- mean.alpha
}
count <- count+1
}
q1 <- apply(Dn,1,function(i)stats::quantile(i,mean.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-mean.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
confband <- cbind(banda1,banda2)
if(plot == TRUE){
gu <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
d <- confband[j,1]
fa <- Fh(a)
return(Fh(t)+d-fa)
} )
hu <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
b <- y[j+1]
f <- confband[j+1,1]
return(gu(t)+(t-a)/(b-a)*(f-gu(b)))
} )
gl <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
d <- confband[j,2]
fa <- Fh(a)
return(Fh(t)+d-fa)
} )
hl <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
b <- y[j+1]
f <- confband[j+1,2]
return(gl(t)+(t-a)/(b-a)*(f-gl(b)))
} )
grid <- seq(y[1],y[k+1],len=500)[-c(1,500)]
grDevices::dev.new(noRStudioGD=TRUE)
graphics::curve(Fh,min(y),max(y),type="n",lwd=2,ylab="Cumulative probability",main="Kernel distribution")
graphics::polygon(c(grid,rev(grid)),c(hl(grid),rev(hu(grid))),col="grey",border=NA)
graphics::curve(Fh,lwd=2,add=T)
graphics::lines(grid,hu(grid),col=2,lty=2)
graphics::lines(grid,hl(grid),col=2,lty=2)
if(!missing(model)){
pmodel <- paste0("p",model)
try(parfit <- fitdistrplus::fitdist(rep(t,ceiling(n*w)),model),silent=T)
if(exists("parfit")){
distr <- get(pmodel)
params <- as.list(parfit$estimate)
pargrid <- seq(min(y),max(y),len=101)
clist <- c(list(q=pargrid),params)
graphics::lines(pargrid, do.call( distr, clist ), col=3, lwd=2 )
}
}
}
return(list(h=h_AMISE,confband=confband,Fh=Fh))
} else {
if(plot == TRUE){
grDevices::dev.new(noRStudioGD=TRUE)
graphics::curve(Fh,min(y),max(y),lwd=2,ylab="Cumulative probability",main="Kernel distribution")
if(!missing(model)){
pmodel <- paste0("p",model)
try(parfit <- fitdistrplus::fitdist(rep(t,ceiling(n*w)),model),silent=T)
if(exists("parfit")){
distr <- get(pmodel)
params <- as.list(parfit$estimate)
pargrid <- seq(min(y),max(y),len=101)
clist <- c(list(q=pargrid),params)
graphics::lines(pargrid, do.call( distr, clist ), col=3, lwd=2 )
}
}
}
if(main == TRUE){
return(list(h=h_AMISE, Fh=Fh))
} else {
return(h=h_AMISE)
}
}
}
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#' Plug-in bandwidth selector for kernel distribution estimation and binned data.
#'
#' @param n Positive integer. Size of the complete sample.
#' @param y Vector. Observed values. They define the extremes of the sequence of intervals in which data is binned.
#' @param w Vector. Proportion of observations within each interval.
#' @param ni Vector. Number of observations within each interval.
#' @param gplugin Positive real number. Pilot bandwidth. If missing, rule-of-thumb bandwidth is considered.
#' @param confband Logical. If TRUE, bootstrap confidence bands for the distribution are constructed. Defaults to FALSE.
#' @param alpha Significance level for the bootstrap confidence bands. Defaults to 0.05.
#' @param B Number of bootstrap resamples. Defaults to 1000.
#' @param type Character. If \code{type} = "N", normality is assumed at the last step when calculating the plug-in bandwidth. If \code{type} = "A", parameter at last step is estimated nonparametrically using \code{gplugin} as bandwidth. Otherwise, the unknown parameter is estimated fitting a normal mixture. Defaults to \code{type} = "N".
#' @param plot Logical. If TRUE, results are plotted. Defaults to TRUE.
#' @param print Logical. If TRUE, script current status is printed. Defaults to TRUE.
#' @param model Character. Name of the parametric family of distributions to be fitted for the grouped sample. Parameters are estimated by maximum likelihood.
#' @param parallel Logical. If TRUE, confidence bands are estimated using parallel computing with sockets.
#' @param pars Environment. Needed for the well functioning of the script. DO NOT modify this argument.
#'
#' @return A list with components
#' \item{h}{Plug-in bandwidth.}
#' \item{Fh}{Function. Kernel distribution estimator with bandwidth \code{h}.}
#' \item{confband}{(Optional) Bootstrap confidence bands for the distribution function.}
#'
#' @examples
#' set.seed(1)
#' n <- 200 #complete sample size
#' k <- 30 #number of intervals
#' x <- rnorm(n,6,1) #complete sample
#' y <- seq(min(x)-0.2,max(x)+0.2,len=k+1) #intervals
#' w <- c(sapply(2:k,function(i)sum( x<y[i]&x>=y[i-1] )), sum(x<=y[k+1]&x>=y[k]) )/n #proportions
#' bw.dist.binned(n,y,w,plot=FALSE)
#'
#' @references
#' \insertRef{TesisMiguel2015}{binnednp}
#'
#' \insertRef{Phalaris2016}{binnednp}
#'
#' @useDynLib binnednp
#' @importFrom Rcpp sourceCpp
#'
#' @export
bw.dist.binned <- function(n,y,w,ni,gplugin,type="N",confband=F,B=1000,alpha=0.05,plot=TRUE,print=TRUE,model,parallel=FALSE,pars=new.env()){
main <- !exists("k", where = pars, inherits = FALSE)
if(main==TRUE){
t <- y[-length(y)]+diff(y)/2
k <- length(t)
if(missing(w)){
if(!missing(ni)){
if(missing(n)) n <- sum(ni)
w <- ni/n
} else {
stop("Arguments w or ni must be provided.")
}
}
if(anyDuplicated(y) != 0){
dup <- which(duplicated(y))
comby <- y[-dup]
lcy <- length(comby)
combw <- numeric(lcy-1)
for(i in 2:lcy){
combw[i-1] <- sum(w[which(y==comby[i])-1])
}
combt <- comby[-lcy]+diff(comby)/2
t <- combt
y <- comby
w <- combw
k <- lcy-1
}
K <- function(x) stats::dnorm(x)
pK <- Vectorize(function(x) stats::pnorm(x))
C0 <- 2*stats::integrate(function(x)x*K(x)*pK(x),-Inf,Inf)$value
l <- mean(diff(y))
K2 <- function(x) (x^2-1)*stats::dnorm(x)
K4 <- function(x) ((x^2-3)*(x^2-1)-2*x^2)*stats::dnorm(x)
K6_0 <- kedd::kernel.fun(0,deriv.order=6,kernel="gaussian")$kx
K8_0 <- kedd::kernel.fun(0,deriv.order=8,kernel="gaussian")$kx
L1 <- function(w,h) -sum( sapply( 1:k,function(i) sum(K2((t[i]-t)/h)*w[i]*w) ) )/h^3 # Af1=-psi2
L2 <- function(w,h) sum( sapply( 1:k,function(i) sum(K4((t[i]-t)/h)*w[i]*w) ) )/h^5 # Af2=psi4
L3 <- function(w,h) -sum( sapply( 1:k,function(i) sum(kedd::kernel.fun((t[i]-t)/h,deriv.order=6,kernel="gaussian")$kx*w[i]*w) ) )/h^7
L4 <- function(w,h) sum( sapply( 1:k,function(i) sum(kedd::kernel.fun((t[i]-t)/h,deriv.order=8,kernel="gaussian")$kx*w[i]*w) ) )/h^9
L5 <- function(w,h) -sum( sapply( 1:k,function(i) sum(kedd::kernel.fun((t[i]-t)/h,deriv.order=10,kernel="gaussian")$kx*w[i]*w) ) )/h^11
} else {
t <- pars$t
k <- pars$k
y <- pars$y
K <- pars$K
pK <- pars$pK
C0 <- pars$C0
l <- pars$l
K2 <- pars$K2
K4 <- pars$K4
K6_0 <- pars$K6_0
K8_0 <- pars$K8_0
L1 <- pars$L1
L2 <- pars$L2
L3 <- pars$L3
L4 <- pars$L4
L5 <- pars$L5
}
mu_hat <- sum(w*t)
sigma_hat <- sqrt( sum(w*(t-mu_hat)^2) )
if(type == "N" || type == "A"){
if(missing(gplugin)) gplugin <- 1.59*sigma_hat*n^(-1/3)
if(type == "A"){
f_gplugin <- Vectorize(function(x)1/gplugin*sum(w*K((x-t)/gplugin)))
llim <- mu_hat-3*sigma_hat
rlim <- mu_hat+3*sigma_hat
Af <- stats::integrate(function(x)f_gplugin(x)^2,llim,rlim)$value
if(!exists("Af")) Af <- stats::integrate(function(x)f_gplugin(x)^2,y[1],y[k+1])$value
psi10 <- -L5(w,gplugin)
} else {
Af <- 1/(2*sqrt(pi)*sigma_hat)
psi10 <- -30240/((2*sigma_hat)^11*sqrt(pi))
}
eta8 <- (-2*K8_0*Af*l/psi10)^(1/11)
psi8 <- L4(w,eta8)
eta6 <- (-2*K6_0*Af*l/psi8)^(1/9)
psi6 <- -L3(w,eta6)
eta4 <- (-2*K4(0)*Af*l/psi6)^(1/7)
psi4 <- L2(w,eta4)
eta2 <- (-2*K2(0)*Af*l/psi4)^(1/5)
Af1 <- L1(w,eta2)
} else {
clustering <- mclust::Mclust(rep(t,n*w),G=1:5,verbose=FALSE,modelNames="V")
mix_params <- clustering$parameters
mu_mixt <- mix_params$mean
sigma_mixt <- sqrt(mix_params$variance$sigmasq)
alfa_mixt <- mix_params$pro
normal_mixt <- nor1mix::norMix(mu=mu_mixt,sigma=sigma_mixt,w=alfa_mixt)
f1_mixt <- Vectorize( function(x) -sum(alfa_mixt*(x-mu_mixt)/sigma_mixt^3*stats::dnorm((x-mu_mixt)/sigma_mixt)) )
mixlim1 <- nor1mix::qnorMix(0.001,normal_mixt)
mixlim2 <- nor1mix::qnorMix(0.999,normal_mixt)
Af1 <- stats::integrate(function(x)f1_mixt(x)^2,mixlim1,mixlim2)$value
}
h_AMISE <- ( C0/(n*Af1) )^(1/3)
if(main == TRUE){
x <- NULL
Fh <- Vectorize( function(x)sum(w*stats::pnorm((x-t)/h_AMISE)) )
}
if(confband == T){
pars$t <- t
pars$k <- k
pars$y <- y
pars$K <- K
pars$pK <- pK
pars$C0 <- C0
pars$l <- l
pars$K2 <- K2
pars$K4 <- K4
pars$K6_0 <- K6_0
pars$K8_0 <- K8_0
pars$L1 <- L1
pars$L2 <- L2
pars$L3 <- L3
pars$L4 <- L4
pars$L5 <- L5
gplugin <- bw.dist.binned.boot(n,y,w,pilot.type=2,print=FALSE)$h
Fhy <- sapply(y, function(x)sum( w*stats::pnorm((x-t)/h_AMISE) ))
Fg <- Vectorize(function(x)sum( w*stats::pnorm((x-t)/gplugin) ))
Fgy <- Fg(y)
Dn <- matrix(0,nrow=length(y),ncol=B)
if(!parallel){
for(b in 1:B){
rx <- sort(sample(t,replace=T,size=n,prob=w)+gplugin*stats::rnorm(n))
wb <- calcw_cpp(rx,y)
h_AMISE_boot <- bw.dist.binned(n,y,wb,plot=FALSE,print=FALSE,type=type,pars=pars)
Fhby <- sapply(y,function(x)sum( wb*stats::pnorm( (x-t)/h_AMISE_boot ) ))
Dn[,b] <- Fhby
if(print == TRUE) cat("\rConstructing bootstrap confidence bands. Progress:",floor(100*b/B),"%")
}
} else {
parfun <- function(b){
rx <- sort(sample(t,replace=T,size=n,prob=w)+gplugin*stats::rnorm(n))
wb <- calcw_cpp(rx,y)
h_AMISE_boot <- bw.dist.binned(n,y,wb,plot=FALSE,print=FALSE,type=type,pars=pars)
Fhby <- sapply(y,function(x)sum( wb*stats::pnorm( (x-t)/h_AMISE_boot ) ))
return(Fhby)
}
ncores <- parallel::detectCores()
cl <- parallel::makeCluster(ncores)
parallel::clusterEvalQ(cl, library(binnednp))
parallel::clusterExport(cl, 'calcw_cpp')
paroutput <- parallel::parSapply(cl, 1:B, parfun)
Dn <- paroutput
parallel::stopCluster(cl)
}
alfa <- alpha/length(y)
count <- 0
maxcount <- 100
low.alpha <- alfa
high.alpha <- alpha
if(print == TRUE) cat("\n")
while(count < maxcount){
if(print == TRUE) cat("\rAdjusting significance level. Progress:",floor(100*(count+1)/maxcount),"%")
mean.alpha <- 0.5*(low.alpha+high.alpha)
q1 <- apply(Dn,1,function(i)stats::quantile(i,low.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-low.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
p_low.alpha <- sapply(1:B,function(b){
aux <- ifelse(Dn[,b] < banda1 && Dn[,b] > banda2,1,0)
return(aux)
})
p_low.alpha <- sum(p_low.alpha)/B
q1 <- apply(Dn,1,function(i)stats::quantile(i,high.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-high.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
p_high.alpha <- sapply(1:B,function(b){
aux <- ifelse(Dn[,b] < banda1 && Dn[,b] > banda2,1,0)
return(aux)
})
p_high.alpha <- sum(p_high.alpha)/B
q1 <- apply(Dn,1,function(i)stats::quantile(i,mean.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-mean.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
p_mean.alpha <- sapply(1:B,function(b){
aux <- ifelse(Dn[,b] < banda1 && Dn[,b] > banda2,1,0)
return(aux)
})
p_mean.alpha <- sum(p_mean.alpha)/B
if(p_mean.alpha >= 1-alpha){
low.alpha <- mean.alpha
} else {
high.alpha <- mean.alpha
}
count <- count+1
}
q1 <- apply(Dn,1,function(i)stats::quantile(i,mean.alpha/2))
q2 <- apply(Dn,1,function(i)stats::quantile(i,1-mean.alpha/2))
banda1 <- pmin(pmax(Fhy+Fgy-q1,0),1)
banda2 <- pmin(pmax(Fhy+Fgy-q2,0),1)
confband <- cbind(banda1,banda2)
if(plot == TRUE){
gu <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
d <- confband[j,1]
fa <- Fh(a)
return(Fh(t)+d-fa)
} )
hu <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
b <- y[j+1]
f <- confband[j+1,1]
return(gu(t)+(t-a)/(b-a)*(f-gu(b)))
} )
gl <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
d <- confband[j,2]
fa <- Fh(a)
return(Fh(t)+d-fa)
} )
hl <- Vectorize( function(t){
j <- max(which(y<t))
a <- y[j]
b <- y[j+1]
f <- confband[j+1,2]
return(gl(t)+(t-a)/(b-a)*(f-gl(b)))
} )
grid <- seq(y[1],y[k+1],len=500)[-c(1,500)]
grDevices::dev.new(noRStudioGD=TRUE)
graphics::curve(Fh,min(y),max(y),type="n",lwd=2,ylab="Cumulative probability",main="Kernel distribution")
graphics::polygon(c(grid,rev(grid)),c(hl(grid),rev(hu(grid))),col="grey",border=NA)
graphics::curve(Fh,lwd=2,add=T)
graphics::lines(grid,hu(grid),col=2,lty=2)
graphics::lines(grid,hl(grid),col=2,lty=2)
if(!missing(model)){
pmodel <- paste0("p",model)
try(parfit <- fitdistrplus::fitdist(rep(t,ceiling(n*w)),model),silent=T)
if(exists("parfit")){
distr <- get(pmodel)
params <- as.list(parfit$estimate)
pargrid <- seq(min(y),max(y),len=101)
clist <- c(list(q=pargrid),params)
graphics::lines(pargrid, do.call( distr, clist ), col=3, lwd=2 )
}
}
}
return(list(h=h_AMISE,confband=confband,Fh=Fh))
} else {
if(plot == TRUE){
grDevices::dev.new(noRStudioGD=TRUE)
graphics::curve(Fh,min(y),max(y),lwd=2,ylab="Cumulative probability",main="Kernel distribution")
if(!missing(model)){
pmodel <- paste0("p",model)
try(parfit <- fitdistrplus::fitdist(rep(t,ceiling(n*w)),model),silent=T)
if(exists("parfit")){
distr <- get(pmodel)
params <- as.list(parfit$estimate)
pargrid <- seq(min(y),max(y),len=101)
clist <- c(list(q=pargrid),params)
graphics::lines(pargrid, do.call( distr, clist ), col=3, lwd=2 )
}
}
}
if(main == TRUE){
return(list(h=h_AMISE, Fh=Fh))
} else {
return(h=h_AMISE)
}
}
}
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