kde: Kernel density estimate

Description

Kernel density estimate for 1- to 6-dimensional data.

Usage

kde(x, H, h, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points, 
    binned=FALSE, bgridsize, positive=FALSE, adj.positive, w,
    compute.cont=TRUE, approx.cont=TRUE, unit.interval=FALSE,
    verbose=FALSE)
# S3 method for kde
predict(object, ..., x, zero.flag=TRUE)

Arguments

matrix of data values

H,h

bandwidth matrix/scalar bandwidth. If these are missing, Hpi or hpi is called by default.

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. Default is FALSE.

bgridsize

vector of binning grid sizes

positive

flag if 1-d data are positive. Default is FALSE.

adj.positive

adjustment applied to positive 1-d data

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 kde

zero.flag

interploted values object$estimate of when x outside of object$eval.points=0 (if TRUE), = nearest object$estimate (if FALSE)

...

other parameters

Value

A kernel density estimate is an object of class kde which is a list with fields:

data points - same as input

eval.points

vector or list of points at which the estimate is evaluated

estimate

density estimate at eval.points

scalar bandwidth (1-d only)

bandwidth matrix

gridtype

"linear"

gridded

flag for estimation on a grid

binned

flag for binned estimation

names

variable names

weights

cont

probability contour levels (if compute.cont=TRUE)

Details

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.

For d=1, 2, 3, 4, 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 conjuction with the plot method.

--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 likelilood), and is not compatible with the plot method.

--For d>4, computing the kernel density estimate over a grid is not feasible, and so it is computed exactly and eval.points (as a matrix) must be specified.

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 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]).

Examples

Run this code

# NOT RUN {
## positive data example
set.seed(8192)
x <- 2^rnorm(100)
fhat <- kde(x=x, positive=TRUE)
plot(fhat, col=3)
points(c(0.5, 1), predict(fhat, x=c(0.5, 1)))

## 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, binned=TRUE, compute.cont=TRUE, xmin=c(-5,-5), xmax=c(5,5), bgridsize=c(151,151))
plot(fhat)

## See other examples in ? plot.kde
# }