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#************************************************************************
# TS Kernel estimator as described in Hirukawas's 2010 paper:
#
# @article{hirukawa2010,
# title = {Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval},
# author = {Hirukawa, M.},
# journal = {Computational Statistics & Data Analysis},
# year = {2010},
# volume = {54},
# number = {2}
# pages = {473--495}
# }
#
#************************************************************************
setClass(
Class = "HirukawaTSKernel",
representation = representation(
c = "numeric"),
prototype = prototype(modified = FALSE),
contains = "Chen99Kernel"
)
setValidity(
Class = "HirukawaTSKernel",
method = function(object) {
if (object@c <= 0 & object@c >= 1){
stop("HirukawaTSKernel, parameter c must be 0<c<1")
}else if (object@b/object@c > 1){
stop("In HirukawaTSKernel density calculations, a Chen99Kernel with parameter b=b/c is used. The provided values for b and c make\n",
"b/c >1 and it must be within the (0,1) interval\n")
}else if (object@modified & object@b/object@c > 0.25){
cat(c("In HirukawaTSKernel density calculations, a Chen99Kernel with parameter b=b/c is used. The provided values for b and c make\n",
"b/c > 0.25 and therefore left and right boundaries overlap which may result in extrange discontinuities in the density function\n"))
}else{}
return(TRUE)
}
)
setGeneric (
name = "getc",
def = function(.Object){standardGeneric("getc")}
)
setMethod(
f = "getc",
signature = "HirukawaTSKernel",
definition = function(.Object) {
.Object@modified
})
setMethod(
f = "density",
signature = "HirukawaTSKernel",
definition = function(x,values,scaled = FALSE) {
.Object <- x
x <- values
isMatrix.x <- is.matrix(x)
#dims = [nrows,ncols]
dims <- dim(x)
if(!scaled){
# scale the data to the 0-1 interval
x <- getScaledPoints(.Object,x)
}
# if any value in x is lower than 0 or grater than 1 its density is 0
numDataPoints <- length(x)
index.nozero <- which(x>=0 & x <=1)
x <- x[index.nozero]
if(length(x) == 0){ # all elements in x were out of bound
return(rep(0,numDataPoints - length(index.nozero)))
}
# x is considered as a vector even if it is a matrix(elements taken by columns)
x.indices <- rep(0,times = length(x))
x.densities <- numeric(0)
if(length(.Object@densityCache) == length(.Object@dataPointsCache)){
# if there are density values calculated in the cache, first we look
# at the cache to check whether some of the values in x have been already calculated
x.indices <- match(x, .Object@dataPointsCache, nomatch=0)
if(any(x.indices > 0)){
# the density of some of the points are already calculated in the cache
x.densities[x.indices != 0] <- .Object@densityCache[x.indices[x.indices!=0]]
}else{}
}else{}
# the data poins whose densities are not calculated in the cache
x.new <- x[x.indices == 0]
x.new.length <- length(x.new)
if(x.new.length > 0){
# There are densities to be calculated
kernel1 <- new(Class="Chen99Kernel",dataPoints=.Object@dataPoints, b=.Object@b, dataPointsCache=.Object@dataPointsCache,
modified=.Object@modified)
kernel2 <- new(Class="Chen99Kernel",dataPoints=.Object@dataPoints, b=.Object@b/.Object@c, dataPointsCache=.Object@dataPointsCache,
modified=.Object@modified)
# x.densities[x.indices == 0] <- density(kernel1,x.new,scaled=TRUE)^(1/(1-.Object@c)) * density(kernel2,x.new,scaled=TRUE)^(-.Object@c/(1-.Object@c))
aux1 <- density(kernel1,x.new,scaled=TRUE)^(1/(1-.Object@c))
aux2 <- density(kernel2,x.new,scaled=TRUE)^(-.Object@c/(1-.Object@c))
aux3 <- aux1 * aux2
# when the estimated density tends to 0 when estimating with the Chen99Kernel (kernel1 or kernel2), it may be possible
# that aux1 -> 0 and aux2 -> inf which results in a NaN. In those cases, the density with HirukawaTSKernel should
# tends alsto to 0
aux3[aux1 == 0] <- 0
x.densities[x.indices == 0] <- aux3
}
else{}
# include the density (density=0) of the out-of-bound x points in the final result
aux.density <- numeric(numDataPoints)
aux.density[index.nozero] <- x.densities
x.densities <- aux.density
#if x is a matrix, we storte the densities as a matrix object
if(isMatrix.x){
dim(x.densities) <- dims
}
#if data are in another scale (not in the [0,1] interval) we should
# normalize the density by dividing it by the length
# of the interval so that the density integrates to 1
domain.length <- .Object@upper.limit - .Object@lower.limit
if(!scaled){
x.densities <- x.densities/domain.length
}
return(x.densities)
}
)
#####################################
## Constructor functions for users ##
#####################################
hirukawaTSKernel <- function(dataPoints, c, b=length(dataPoints)^(-2/5), dataPointsCache=NULL, modified = FALSE, lower.limit=0,upper.limit=1){
#cat("~~~~~~ HirukawaTSKernel: constructor ~~~~~~\n")
dataPoints.scaled <- dataPoints
dataPointsCache.scaled <- dataPointsCache
if(is.null(dataPointsCache)){
dataPointsCache.scaled <- seq(0,1,0.01)
}
if(lower.limit!=0 || upper.limit!=1){
dataPoints.scaled <- (dataPoints-lower.limit)/(upper.limit-lower.limit)
if(!is.null(dataPointsCache)){
dataPointsCache.scaled <- (dataPointsCache-lower.limit)/(upper.limit-lower.limit)
}
}
kernel <- new(Class="HirukawaTSKernel",dataPoints = dataPoints.scaled, b = b, dataPointsCache = dataPointsCache.scaled, modified = modified, c = c, lower.limit=lower.limit,upper.limit=upper.limit)
setDensityCache(kernel, densityFunction=NULL)
return(kernel)
}
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