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: kalman
See also: rICfil calibrIC ICerz

Quantlet: numint2
Description: Auxiliary routine for rICfil: calculates for dimension p=2 diag(E[ YY' u min(b/|aIhY|,u) ]) and diag(E[ YY' min(b/|aIhY|,u)^2 ]) for u square root of a Chi^2_2-variable, and Y~ufo(S_2) indep of u by using a polar representation of Lambda:= I^{1/2} Y u, u = | I^{-1/2} Lambda |, Y=I^{-1/2} Lambda /u the integrals are evaluated stepwise, first conditioning on Y and calculated "analytically" using Ewinn, Ew2inn and then the outer integration is done by a Romberg-Procedure along the directions Y, parametrized by a sin-cos-representation.

Usage: {r,s}=numint2(aIh,b,N)
Input:
aIh dim: 2; diag. of Eigenvalues of A I^{1/2}, I Fisher-Information (>=0)
b numeric; clipping height (>0)
N numeric; number of gridpoints for Integration
Output:
r 2-dim ; r=diag(E[ YY' u min(b/|aIhY|,u) ])
s 2-dim; s=diag(E[ YY' min(b/|aIhY|,u)^2 ])

Note:

Example:
to be looked up in rICfil

Result:
n/a



Author: P. Ruckdeschel, 19991010
(C) MD*TECH Method and Data Technologies, 05.02.2006