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 ICerzsep

Quantlet: numint2m
Description: Auxiliary routine for rICfil: calculates for dimension p=2 (E[ YY' u min(b/|aIhY|,u) ]) and (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}=numint2m(aIh,b,N)
Input:
aIh 2 x 2-dim; A I^{1/2}, I Fisher-Information; sym. pos. semidef!
b numeric; clipping height >0
N numeric; number of gridpoints for Integration
Output:
r 2 x 2-dim ; r=(E[ YY' u min(b/|aIhY|,u) ])
s 2 x 2-dim; s=(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