hdrcde (version 3.4)

cde: Conditional Density Estimation

Description

Calculates kernel conditional density estimate using local polynomial estimation.

Usage

cde(
  x,
  y,
  deg = 0,
  link = "identity",
  a,
  b,
  mean = NULL,
  x.margin,
  y.margin,
  x.name,
  y.name,
  use.locfit = FALSE,
  fw = TRUE,
  rescale = TRUE,
  nxmargin = 15,
  nymargin = 100,
  a.nndefault = 0.3,
  ...
)

Arguments

x

Numerical vector or matrix: the conditioning variable(s).

y

Numerical vector: the response variable.

deg

Degree of local polynomial used in estimation.

link

Link function used in estimation. Default "identity". The other possibility is "log" which is recommended if degree > 0.

a

Optional bandwidth in x direction.

b

Optional bandwidth in y direction.

mean

Estimated mean of y|x. If present, it will adjust conditional density to have this mean.

x.margin

Values in x-space on which conditional density is calculated. If not specified, an equi-spaced grid of nxmargin values over the range of x is used. If x is a matrix, x.margin should be a list of two numerical vectors.

y.margin

Values in y-space on which conditional density is calculated. If not specified, an equi-spaced grid of nymargin values over the range of y is used.

x.name

Optional name of x variable used in plots.

y.name

Optional name of y variable used in plots.

use.locfit

If TRUE, will use locfit for estimation. Otherwise ksmooth is used. locfit is used if degree>0 or link not the identity or the dimension of x is greater than 1 even if use.locfit=FALSE.

fw

If TRUE (default), will use fixed window width estimation. Otherwise nearest neighbourhood estimation is used. If the dimension of x is greater than 1, nearest neighbourhood must be used.

rescale

If TRUE (default), will rescale the conditional densities to integrate to one.

nxmargin

Number of values used in x.margin by default.

nymargin

Number of values used in y.margin by default.

a.nndefault

Default nearest neighbour bandwidth (used only if fw=FALSE and a is missing.).

…

Additional arguments are passed to locfit.

Value

A list with the following components:

x

grid in x direction on which density evaluated. Equal to x.margin if specified.

y

grid in y direction on which density is evaluated. Equal to y.margin if specified.

z

value of conditional density estimate returned as a matrix.

a

window width in x direction.

b

window width in y direction.

x.name

Name of x variable to be used in plots.

y.name

Name of y variable to be used in plots.

Details

If bandwidths are omitted, they are computed using normal reference rules described in Bashtannyk and Hyndman (2001) and Hyndman and Yao (2002). Bias adjustment uses the method described in Hyndman, Bashtannyk and Grunwald (1996). If deg>1 then estimation is based on the local parametric estimator of Hyndman and Yao (2002).

References

Hyndman, R.J., Bashtannyk, D.M. and Grunwald, G.K. (1996) "Estimating and visualizing conditional densities". Journal of Computational and Graphical Statistics, 5, 315-336.

Bashtannyk, D.M., and Hyndman, R.J. (2001) "Bandwidth selection for kernel conditional density estimation". Computational statistics and data analysis, 36(3), 279-298.

Hyndman, R.J. and Yao, Q. (2002) "Nonparametric estimation and symmetry tests for conditional density functions". Journal of Nonparametric Statistics, 14(3), 259-278.

See Also

cde.bandwidths

Examples

# NOT RUN {
# Old faithful data
faithful.cde <- cde(faithful$waiting, faithful$eruptions,
  x.name="Waiting time", y.name="Duration time")
plot(faithful.cde)
plot(faithful.cde, plot.fn="hdr")

# Melbourne maximum temperatures with bias adjustment
x <- maxtemp[1:3649]
y <- maxtemp[2:3650]
maxtemp.cde <- cde(x, y,
  x.name="Today's max temperature", y.name="Tomorrow's max temperature")
# Assume linear mean
fit <- lm(y~x)
fit.mean <- list(x=6:45,y=fit$coef[1]+fit$coef[2]*(6:45))
maxtemp.cde2 <- cde(x, y, mean=fit.mean,
	 x.name="Today's max temperature", y.name="Tomorrow's max temperature")
plot(maxtemp.cde)
# }