XploRe Help : canbw

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:	uni tri trian epa qua gau cosi canker

Quantlet:		canbw
Description:		computes canonical bandwidth and squared L2 norm for a univariate kernel function K.

Reference(s):

Marron, J.S. and Nolan, D. (1988). Canonical kernels for density estimation. Statistics and Probability Letters, 7, pp. 195-199. Haerdle, W. (1991). Smoothing Techniques. With Implementations in S. Springer, New York, p. 220.

Usage:	`{dK, cK, mK} = canbw(K)`
Input:
	`K`	string, kernel function on [-1,1] or Gaussian kernel "gau"
Output:
	`dK`	scalar, canonical bandwidth for K.
	`cK`	scalar, squared L2 norm of K.
	`mK`	scalar, second moment of K.

Note:

For kernels "uni", "trian", "epa", "qua", "tri", "gau" and "cosi", the exact values are returned, otherwise a numerical approximation is used.

Example:

library("smoother") {dK, cK, mK} = canbw("qua") dK ~ 35^0.2 ; dK should be 35^0.2 cK ~ 5/7 ; cK should be 5/7 mK ~ 1/7 ; mK should be 1/7

Result:

Contents of _tmp
[1,]   2.0362   2.0362

Contents of _tmp
[1,]  0.71429  0.71429

Contents of _tmp
[1,]  0.14286  0.14286

Author: M. Mueller, 20020915