Bandwidth calculation for conditional density estimation

Calculates bandwidths for kernel conditional density estimates. Methods described in Bashtannyk and Hyndman (2001) and Hyndman and Yao (2002).

Usage

cde.bandwidths(
  x,
  y,
  deg = 0,
  link = "identity",
  method = 1,
  y.margin,
  passes = 2,
  ngrid = 8,
  min.a = NULL,
  ny = 25,
  use.sample = FALSE,
  GCV = TRUE,
  b = NULL,
  ...
)

Arguments

x

Numerical vector: the conditioning variable.

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.

method

method = 1:: Hyndman-Yao algorithm if deg>0; Bashtannyk-Hyndman algorithm if deg=0;
method = 2:: Normal reference rules;
method = 3:: Bashtannyk-Hyndman regression method if deg=0;
method = 4:: Bashtannyk-Hyndman bootstrap method if deg=0.

y.margin

Values in y-space on which conditional density is calculated. If not specified, an equi-spaced grid of 50 values over the range of y is used.

passes

Number of passes through Bashtannyk-Hyndman algorithm.

ngrid

Number of values of smoothing parameter in grid.

min.a

Smallest value of a to consider if method=1.

ny

Number of values to use for y margin if y.margin is missing.

use.sample

Used when regression method (3) is chosen.

GCV

Generalized cross-validation. Used only if method=1 and deg>0. If GCV=FALSE, method=1 and deg=0, then the AIC is used instead. The argument is ignored if deg=0 or method>1.

b

Value of b can be specified only if method=1 and deg>0. For deg=0 or method>1, this argument is ignored.

...

Other arguments control details for individual methods.

Value

a: Window width in x direction.
b: Window width in y direction.

Details

Details of the various algorithms are in Bashtannyk and Hyndman (2001) and 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.

Author

Rob J Hyndman

Examples

bands <- cde.bandwidths(faithful$waiting,faithful$eruptions,method=2)
plot(cde(faithful$waiting,faithful$eruptions,a=bands$a,b=bands$b))