Nothing
R/MCV.R
In kedd: Kernel Estimator and Bandwidth Selection for Density and Its Derivatives
## Wed Jun 19 14:21:28 2013
## Original file Copyright 2013 A.C. Guidoum
## This file is part of the R package kedd.
## Arsalane Chouaib GUIDOUM <acguidoum@usthb.dz> and <starsalane@gmail.com>
## Department of Probabilities-Statistics
## Faculty of Mathematics
## University of Science and Technology Houari Boumediene
## BP 32 El-Alia, U.S.T.H.B, Algeris
## Algeria
##############################################################################
## Modified Cross-Validation (MCV)
h.mcv <- function(x, ...) UseMethod("h.mcv")
h.mcv.default <- function(x,deriv.order=0,lower=0.1*hos,upper=2*hos,tol=0.1 * lower,
kernel=c("gaussian","epanechnikov","triweight","tricube",
"biweight","cosine"),...)
{
if (!is.numeric(x) || length(dim(x)) >=1 || length(x) < 3L)
stop("argument 'x' must be numeric and need at least 3 data points")
if (any(deriv.order < 0 || deriv.order != round(deriv.order)))
stop("argument 'deriv.order' is non-negative integers")
if (missing(kernel)) kernel <- "gaussian"
r <- deriv.order
name <- deparse(substitute(x))
x <- x[!is.na(x)]
x <- sort(x)
n <- length(x)
if (kernel=="epanechnikov" && (2*r) + 2 >= 3) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
else if (kernel=="triweight" && (2*r) + 2 >= 7) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
else if (kernel=="biweight" && (2*r) + 2 >= 5) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
else if (kernel=="tricube" && (2*r) + 2 >= 10) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
hos <- ((243 *(2*r+1)*A3_kMr(kernel,r))/(35* A2_kM(kernel)^2))^(1/(2*r+5)) * sd(x,na.rm = TRUE) * n^(-1/(2*r+5))
if (!is.numeric(upper)){
stop("argument 'upper' must be numeric. Default 2*hos (Oversmoothing) boundary was used")
upper= 2*hos
}
if (!is.numeric(lower)){
stop("argument 'lower' must be numeric. Default 0.1*hos boundary was used")
lower=0.1*hos
}
if (lower < 0 | lower >= upper){
stop("the boundaries must be positive and 'lower' must be smaller than 'upper'. Default boundaries were used")
upper=2*hos
lower=0.1*hos
}
R_Kr1 <- A3_kMr(kernel,r)
fmcv <- function(h)
{
L1 <- kernel_fun_conv(kernel,outer(x,x,"-")/h,deriv.order=r)
diag(L1) <- 0
L2 <- ((-1)^(r)/((n-1)*h^(2*r+1)))* colSums(L1)
Q1 <- mean(L2)
D1 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r)
diag(D1) <- 0
D2 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D1)
Q2 <- mean(D2)
D3 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r+2)
diag(D3) <- 0
D4 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D3)
Q3 <- mean(D4)
(1/(n*h^(2*r+1)))* R_Kr1 + Q1 - Q2 - 0.5 * A2_kM(kernel) * Q3
}
obj <- optimize(fmcv , c(lower, upper),tol=tol)
structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r,h = obj$minimum ,
min.mcv=obj$objective),class="h.mcv")
}
######
print.h.mcv <- function(x, digits=NULL, ...)
{
class(x) <- "h.mcv"
cat("\nCall:\t","\tModified Cross-Validation","\n",
"\nDerivative order = ",x$deriv.order,
"\nData: ",x$data.name," (",x$n," obs.);","\tKernel: ",x$kernel,
"\nMin MCV = ",format(x$min.mcv,digits=digits),";","\tBandwidth 'h' = ",format(x$h,digits=digits), "\n\n",sep="")
invisible(x)
}
######
plot.mcv <- function(f,seq.bws=NULL,main=NULL,sub = NULL, xlab=NULL, ylab=NULL,
type="l",las=1,lwd=1,...)
{
class(f) <- "h.mcv"
r <- f$deriv.order
n <- f$n
kernel <- f$kernel
x <- sort(f$x)
if (kernel=="epanechnikov" && (2*r) + 2 >= 3) stop(" 'epanechnikov kernel derivative = 0' for '(2 * order) + 2 >= 3' ")
else if (kernel=="triweight" && (2*r) + 2 >= 7) stop(" 'triweight kernel derivative = 0' for '(2 * order) + 2 >= 7' ")
else if (kernel=="biweight" && (2*r) + 2 >= 5) stop(" 'biweight kernel derivative = 0' for '(2 * order) + 2 >= 5' ")
else if (kernel=="tricube" && (2*r) + 2 >= 10) stop(" 'tricube kernel derivative = 0' for '(2 * order) + 2 >= 10' ")
if(is.null(xlab)) xlab <- "Bandwidths"
if(is.null(ylab)) ylab <- bquote(MCV~(h[(.(r))]))
if(is.null(main)){
if(r !=0) {main <- "Modified Cross-Validation function for \nBandwidth Choice for Density Derivative"}else{
main <- "Modified Cross-Validation function for \nBandwidth Choice for Density Function"}
}
if(is.null(sub)) sub <- paste("Kernel",kernel,";","Derivative order = ",r)
if(is.null(seq.bws)){
hos <- ((243 *(2*r+1)*A3_kMr(kernel,r))/(35* A2_kM(kernel)^2))^(1/(2*r+5)) * sd(x,na.rm = TRUE) * n^(-1/(2*r+5))
seq.bws <- seq(0.15*hos,2*hos,length=50)
}
R_Kr1 <- A3_kMr(kernel,r)
fmcv <- function(h)
{
L1 <- kernel_fun_conv(kernel,outer(x,x,"-")/h,deriv.order=r)
diag(L1) <- 0
L2 <- ((-1)^(r)/((n-1)*h^(2*r+1)))* colSums(L1)
Q1 <- mean(L2)
D1 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r)
diag(D1) <- 0
D2 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D1)
Q2 <- mean(D2)
D3 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r+2)
diag(D3) <- 0
D4 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D3)
Q3 <- mean(D4)
(1/(n*h^(2*r+1)))* R_Kr1 + Q1 - Q2 - 0.5 * A2_kM(kernel) * Q3
}
D <- lapply(1:length(seq.bws), function(i) fmcv(seq.bws[i]))
Minf <- c(do.call("rbind",D))
plot.default(seq.bws,Minf,type=type,las=las,lwd=lwd,xlab=xlab,ylab=ylab,
main=main,sub=sub,font.main=2,cex.main=0.9,font.sub=2,cex.sub=0.7,...)
return(list(kernel=kernel,deriv.order=r,seq.bws=seq.bws, mcv=Minf))
}
plot.h.mcv <- function(x,seq.bws=NULL,...) plot.mcv(x,seq.bws,...)
#####
lines.mcv <- function(f,seq.bws=NULL,...)
{
class(f) <- "h.mcv"
r <- f$deriv.order
n <- f$n
kernel <- f$kernel
x <- sort(f$x)
if (kernel=="epanechnikov" && (2*r) + 2 >= 3) stop(" 'epanechnikov kernel derivative = 0' for '(2 * order) + 2 >= 3' ")
else if (kernel=="triweight" && (2*r) + 2 >= 7) stop(" 'triweight kernel derivative = 0' for '(2 * order) + 2 >= 7' ")
else if (kernel=="biweight" && (2*r) + 2 >= 5) stop(" 'biweight kernel derivative = 0' for '(2 * order) + 2 >= 5' ")
else if (kernel=="tricube" && (2*r) + 2 >= 10) stop(" 'tricube kernel derivative = 0' for '(2 * order) + 2 >= 10' ")
if(is.null(seq.bws)){
hos <- ((243 *(2*r+1)*A3_kMr(kernel,r))/(35* A2_kM(kernel)^2))^(1/(2*r+5)) * sd(x,na.rm = TRUE) * n^(-1/(2*r+5))
seq.bws <- seq(0.15*hos,2*hos,length=50)
}
R_Kr1 <- A3_kMr(kernel,r)
fmcv <- function(h)
{
L1 <- kernel_fun_conv(kernel,outer(x,x,"-")/h,deriv.order=r)
diag(L1) <- 0
L2 <- ((-1)^(r)/((n-1)*h^(2*r+1)))* colSums(L1)
Q1 <- mean(L2)
D1 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r)
diag(D1) <- 0
D2 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D1)
Q2 <- mean(D2)
D3 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r+2)
diag(D3) <- 0
D4 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D3)
Q3 <- mean(D4)
(1/(n*h^(2*r+1)))* R_Kr1 + Q1 - Q2 - 0.5 * A2_kM(kernel) * Q3
}
D <- lapply(1:length(seq.bws), function(i) fmcv(seq.bws[i]))
Minf <- c(do.call("rbind",D))
lines.default(seq.bws,Minf,...)
invisible(NULL)
}
lines.h.mcv <- function(x,seq.bws=NULL,...) lines.mcv(x,seq.bws,...)
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## Wed Jun 19 14:21:28 2013
## Original file Copyright 2013 A.C. Guidoum
## This file is part of the R package kedd.
## Arsalane Chouaib GUIDOUM <acguidoum@usthb.dz> and <starsalane@gmail.com>
## Department of Probabilities-Statistics
## Faculty of Mathematics
## University of Science and Technology Houari Boumediene
## BP 32 El-Alia, U.S.T.H.B, Algeris
## Algeria
##############################################################################
## Modified Cross-Validation (MCV)
h.mcv <- function(x, ...) UseMethod("h.mcv")
h.mcv.default <- function(x,deriv.order=0,lower=0.1*hos,upper=2*hos,tol=0.1 * lower,
kernel=c("gaussian","epanechnikov","triweight","tricube",
"biweight","cosine"),...)
{
if (!is.numeric(x) || length(dim(x)) >=1 || length(x) < 3L)
stop("argument 'x' must be numeric and need at least 3 data points")
if (any(deriv.order < 0 || deriv.order != round(deriv.order)))
stop("argument 'deriv.order' is non-negative integers")
if (missing(kernel)) kernel <- "gaussian"
r <- deriv.order
name <- deparse(substitute(x))
x <- x[!is.na(x)]
x <- sort(x)
n <- length(x)
if (kernel=="epanechnikov" && (2*r) + 2 >= 3) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
else if (kernel=="triweight" && (2*r) + 2 >= 7) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
else if (kernel=="biweight" && (2*r) + 2 >= 5) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
else if (kernel=="tricube" && (2*r) + 2 >= 10) return(structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r, h = NA ,min.mcv=NA),class="h.mcv"))
hos <- ((243 *(2*r+1)*A3_kMr(kernel,r))/(35* A2_kM(kernel)^2))^(1/(2*r+5)) * sd(x,na.rm = TRUE) * n^(-1/(2*r+5))
if (!is.numeric(upper)){
stop("argument 'upper' must be numeric. Default 2*hos (Oversmoothing) boundary was used")
upper= 2*hos
}
if (!is.numeric(lower)){
stop("argument 'lower' must be numeric. Default 0.1*hos boundary was used")
lower=0.1*hos
}
if (lower < 0 | lower >= upper){
stop("the boundaries must be positive and 'lower' must be smaller than 'upper'. Default boundaries were used")
upper=2*hos
lower=0.1*hos
}
R_Kr1 <- A3_kMr(kernel,r)
fmcv <- function(h)
{
L1 <- kernel_fun_conv(kernel,outer(x,x,"-")/h,deriv.order=r)
diag(L1) <- 0
L2 <- ((-1)^(r)/((n-1)*h^(2*r+1)))* colSums(L1)
Q1 <- mean(L2)
D1 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r)
diag(D1) <- 0
D2 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D1)
Q2 <- mean(D2)
D3 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r+2)
diag(D3) <- 0
D4 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D3)
Q3 <- mean(D4)
(1/(n*h^(2*r+1)))* R_Kr1 + Q1 - Q2 - 0.5 * A2_kM(kernel) * Q3
}
obj <- optimize(fmcv , c(lower, upper),tol=tol)
structure(list(x=x, data.name=name,n=n, kernel=kernel, deriv.order=r,h = obj$minimum ,
min.mcv=obj$objective),class="h.mcv")
}
######
print.h.mcv <- function(x, digits=NULL, ...)
{
class(x) <- "h.mcv"
cat("\nCall:\t","\tModified Cross-Validation","\n",
"\nDerivative order = ",x$deriv.order,
"\nData: ",x$data.name," (",x$n," obs.);","\tKernel: ",x$kernel,
"\nMin MCV = ",format(x$min.mcv,digits=digits),";","\tBandwidth 'h' = ",format(x$h,digits=digits), "\n\n",sep="")
invisible(x)
}
######
plot.mcv <- function(f,seq.bws=NULL,main=NULL,sub = NULL, xlab=NULL, ylab=NULL,
type="l",las=1,lwd=1,...)
{
class(f) <- "h.mcv"
r <- f$deriv.order
n <- f$n
kernel <- f$kernel
x <- sort(f$x)
if (kernel=="epanechnikov" && (2*r) + 2 >= 3) stop(" 'epanechnikov kernel derivative = 0' for '(2 * order) + 2 >= 3' ")
else if (kernel=="triweight" && (2*r) + 2 >= 7) stop(" 'triweight kernel derivative = 0' for '(2 * order) + 2 >= 7' ")
else if (kernel=="biweight" && (2*r) + 2 >= 5) stop(" 'biweight kernel derivative = 0' for '(2 * order) + 2 >= 5' ")
else if (kernel=="tricube" && (2*r) + 2 >= 10) stop(" 'tricube kernel derivative = 0' for '(2 * order) + 2 >= 10' ")
if(is.null(xlab)) xlab <- "Bandwidths"
if(is.null(ylab)) ylab <- bquote(MCV~(h[(.(r))]))
if(is.null(main)){
if(r !=0) {main <- "Modified Cross-Validation function for \nBandwidth Choice for Density Derivative"}else{
main <- "Modified Cross-Validation function for \nBandwidth Choice for Density Function"}
}
if(is.null(sub)) sub <- paste("Kernel",kernel,";","Derivative order = ",r)
if(is.null(seq.bws)){
hos <- ((243 *(2*r+1)*A3_kMr(kernel,r))/(35* A2_kM(kernel)^2))^(1/(2*r+5)) * sd(x,na.rm = TRUE) * n^(-1/(2*r+5))
seq.bws <- seq(0.15*hos,2*hos,length=50)
}
R_Kr1 <- A3_kMr(kernel,r)
fmcv <- function(h)
{
L1 <- kernel_fun_conv(kernel,outer(x,x,"-")/h,deriv.order=r)
diag(L1) <- 0
L2 <- ((-1)^(r)/((n-1)*h^(2*r+1)))* colSums(L1)
Q1 <- mean(L2)
D1 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r)
diag(D1) <- 0
D2 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D1)
Q2 <- mean(D2)
D3 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r+2)
diag(D3) <- 0
D4 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D3)
Q3 <- mean(D4)
(1/(n*h^(2*r+1)))* R_Kr1 + Q1 - Q2 - 0.5 * A2_kM(kernel) * Q3
}
D <- lapply(1:length(seq.bws), function(i) fmcv(seq.bws[i]))
Minf <- c(do.call("rbind",D))
plot.default(seq.bws,Minf,type=type,las=las,lwd=lwd,xlab=xlab,ylab=ylab,
main=main,sub=sub,font.main=2,cex.main=0.9,font.sub=2,cex.sub=0.7,...)
return(list(kernel=kernel,deriv.order=r,seq.bws=seq.bws, mcv=Minf))
}
plot.h.mcv <- function(x,seq.bws=NULL,...) plot.mcv(x,seq.bws,...)
#####
lines.mcv <- function(f,seq.bws=NULL,...)
{
class(f) <- "h.mcv"
r <- f$deriv.order
n <- f$n
kernel <- f$kernel
x <- sort(f$x)
if (kernel=="epanechnikov" && (2*r) + 2 >= 3) stop(" 'epanechnikov kernel derivative = 0' for '(2 * order) + 2 >= 3' ")
else if (kernel=="triweight" && (2*r) + 2 >= 7) stop(" 'triweight kernel derivative = 0' for '(2 * order) + 2 >= 7' ")
else if (kernel=="biweight" && (2*r) + 2 >= 5) stop(" 'biweight kernel derivative = 0' for '(2 * order) + 2 >= 5' ")
else if (kernel=="tricube" && (2*r) + 2 >= 10) stop(" 'tricube kernel derivative = 0' for '(2 * order) + 2 >= 10' ")
if(is.null(seq.bws)){
hos <- ((243 *(2*r+1)*A3_kMr(kernel,r))/(35* A2_kM(kernel)^2))^(1/(2*r+5)) * sd(x,na.rm = TRUE) * n^(-1/(2*r+5))
seq.bws <- seq(0.15*hos,2*hos,length=50)
}
R_Kr1 <- A3_kMr(kernel,r)
fmcv <- function(h)
{
L1 <- kernel_fun_conv(kernel,outer(x,x,"-")/h,deriv.order=r)
diag(L1) <- 0
L2 <- ((-1)^(r)/((n-1)*h^(2*r+1)))* colSums(L1)
Q1 <- mean(L2)
D1 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r)
diag(D1) <- 0
D2 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D1)
Q2 <- mean(D2)
D3 <- kernel_fun_der(kernel, outer(x,x,"-")/h,deriv.order=2*r+2)
diag(D3) <- 0
D4 <- ((-1)^r / ((n-1)*h^(2*r+1)))* colSums(D3)
Q3 <- mean(D4)
(1/(n*h^(2*r+1)))* R_Kr1 + Q1 - Q2 - 0.5 * A2_kM(kernel) * Q3
}
D <- lapply(1:length(seq.bws), function(i) fmcv(seq.bws[i]))
Minf <- c(do.call("rbind",D))
lines.default(seq.bws,Minf,...)
invisible(NULL)
}
lines.h.mcv <- function(x,seq.bws=NULL,...) lines.mcv(x,seq.bws,...)
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