XploRe Help : denbwcrit

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	smoother
See also:	denbwsel denrot denest

Quantlet:		denbwcrit
Description:		determines from a range of bandwidths the optimal one using one of the following bandwidth selection criteria: Least Squares Cross Validation (lscv), Biased Cross Validation (bcv), Smoothed Cross Validation (scv), Jones, Marron and Park Cross Validation (jmp), Park and Marron Plug-in (pm), Sheather and Jones Plug-in (sj), and Silverman's rule of thumb.

Reference(s):

Park, B. V. and Turlach, B. A. (1992). Practical Performance of Several Data Driven Bandwidth Selectors. Computational Statistics, 7: pp. 251-270. Haerdle, W. (1991). Smoothing Techniques. With Implementations in S. Springer, New York, p. 220. Haerdle, Mueller, Sperlich, Werwatz (1999): Non- and Semiparametric Modelling. XploRe e-book.

Usage:	`{hopt, ch} = denbwcrit(crit, x, h {,K} {,d} )`
Input:
	`crit`	string, criterion for bandwidth selection: "lscv" = Least Squares Cross Validation, "bcv" = Biased Cross Validation, "scv" = Smoothed Cross Validation, "jmp" = Jones, Marron and Park Cross Validation, "pm" = Park and Marron Plug-in, "sj" = Sheather and Jones Plug-in
	`x`	n x 1 vector, the data.
	`h`	m x 1 vector of bandwidths.
	`K`	optional string representing the kernel function on [-1,1]; default = "gau".
	`d`	optional scalar, discretization binwidth. d must be smaller than h. If not given, the minimum of min(h)/3 and (max(x)-min(x))/200 is used.
Output:
	`hopt`	scalar, optimal bandwidth. (If negative in case of "pm" or "sj", denbwcrit needs to be run again with different range of h.)
	`ch`	m x 2 vector, the criterion function for h values.

Note:

Internally, the Gaussian kernel is used for all computations. If a different kernel function K is given as input, the asymptotical equivalent bandwidth for K is calculated via the canonical kernel approach.

Example:

library("smoother") randomize(111) x=normal(500) h=grid(0.05,0.1,10) {hopt,ch}=denbwcrit("lscv",x,h) hopt library("plot") ch=setmask(ch,"line","blue") plot(ch) setgopt(plotdisplay,1,1,"title",string("hopt=%1.6g",hopt))

Result:

Contents of hopt
[1,]     0.35

hopt is the LSCV optimal bandwidth for these data.
The resulting curve for the LSCV criterion is plotted.

Author: M. Bianchi, S. Klinke, L. Yang, M. Mueller, 20020915 license MD*Tech