Kernel density estimate
Kernel density estimate for 1- to 6-dimensional data.
kde(x, H, h, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points,
binned, bgridsize, positive=FALSE, adj.positive, w,
compute.cont=TRUE, approx.cont=TRUE, unit.interval=FALSE,
verbose=FALSE)
## S3 method for class 'kde'
predict(object, ..., x, zero.flag=TRUE)x |
matrix of data values |
H,h |
bandwidth matrix/scalar bandwidth. If these are missing, |
gridsize |
vector of number of grid points |
gridtype |
not yet implemented |
xmin,xmax |
vector of minimum/maximum values for grid |
supp |
effective support for standard normal |
eval.points |
vector or matrix of points at which estimate is evaluated |
binned |
flag for binned estimation. |
bgridsize |
vector of binning grid sizes |
positive |
flag if data are positive (1-d, 2-d). Default is FALSE. |
adj.positive |
adjustment applied to positive 1-d data |
w |
vector of weights. Default is a vector of all ones. |
compute.cont |
flag for computing 1% to 99% probability contour levels. Default is TRUE. |
approx.cont |
flag for computing approximate probability contour levels. Default is TRUE. |
unit.interval |
flag if 1-d data are bounded on unit interval [0,1]. Default is FALSE. |
verbose |
flag to print out progress information. Default is FALSE. |
object |
object of class |
zero.flag |
interpolated values of |
... |
other parameters |
For d=1, if h is missing, the default bandwidth is hpi.
For d>1, if H is missing, the default is Hpi.
For d=1, if positive=TRUE then x is transformed to
log(x+adj.positive) where the default adj.positive is
the minimum of x. This is known as a log transformation density
estimate.
For d=1, 2, 3, and if eval.points is not specified, then the
density estimate is computed over a grid
defined by gridsize (if binned=FALSE) or
by bgridsize (if binned=TRUE). This form is suitable for
visualisation in conjunction with the plot method.
For d=4, 5, 6, and if eval.points is not specified, then the
density estimate is computed over a grid defined by gridsize.
If eval.points is specified, as a vector (d=1) or
as a matrix (d=2, 3, 4), then the density estimate is computed at
eval.points. This form is suitable for numerical summaries
(e.g. maximum likelihood), and is not compatible with the plot
method. Despite that the density estimate is returned only at
eval.points, by default, a binned gridded estimate is
calculated first and then the density estimate at eval.points
is computed using the predict method. If this default intermediate
binned grid estimate is not required, then set binned=FALSE to
compute directly the exact density estimate at eval.points.
Binned kernel estimation is an approximation to the exact kernel
estimation and is available for d=1, 2, 3, 4. This makes
kernel estimators feasible for large samples. The default value of the
binning flag binned is n>1 (d=1), n>500 (d=2), n>1000 (d>=3).
The default bgridsize,gridsize are d=1: 401; d=2: rep(151, 2); d=3:
rep(51, 3); d=4: rep(21, 4).
The effective support for a normal kernel is where
all values outside [-supp,supp]^d are zero.
The default xmin is min(x)-Hmax*supp and xmax
is max(x)+Hmax*supp where Hmax is the maximum of the
diagonal elements of H. The grid produced is the outer
product of c(xmin[1], xmax[1]), ..., c(xmin[d], xmax[d]).
A kernel density estimate is an object of class kde which is a
list with fields:
x |
data points - same as input |
eval.points |
vector or list of points at which the estimate is evaluated |
estimate |
density estimate at |
h |
scalar bandwidth (1-d only) |
H |
bandwidth matrix |
gridtype |
"linear" |
gridded |
flag for estimation on a grid |
binned |
flag for binned estimation |
names |
variable names |
w |
vector of weights |
cont |
vector of probability contour levels |
## positive data example data(worldbank) wb <- as.matrix(na.omit(worldbank[,2:3])) wb[,2] <- wb[,2]/1000 fhat <- kde(x=wb) fhat.trans <- kde(x=wb, adj.positive=c(0,0), positive=TRUE) plot(fhat, xlim=c(0,20), ylim=c(0,80)) plot(fhat.trans, add=TRUE, col=2) rect(0,0,100,100, lty=2) ## large data example on non-default grid ## 151 x 151 grid = [-5,-4.933,..,5] x [-5,-4.933,..,5] set.seed(8192) x <- rmvnorm.mixt(10000, mus=c(0,0), Sigmas=invvech(c(1,0.8,1))) fhat <- kde(x=x, compute.cont=TRUE, xmin=c(-5,-5), xmax=c(5,5), bgridsize=c(151,151)) plot(fhat) ## See other examples in ? plot.kde
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