| Library: | kalman |
| See also: | rICfil calibrIC |
| Quantlet: | ICerz | |
| Description: | Auxiliary routine for rICfil: - if possible - generates for Scores Lambda~N(0,FI) (FI:: Fisher-Info) a Hampel-Krasker-IC psi to efficiency loss e, i.e. E psi Lambda' = unit(p) E psi=0 (1) E |psi|^2= (1+e) tr (FI^{-1}) (2) and psi= A Lambda w_b w_b=min(1,b/|A Lambda|) for dim p==1 a Newton-Algo is used for both a and b, for dim p>=2 for A a fixed-point-algorithm and for b a "careful" bisection method is used. Integration for A and p==2 is done by a Romberg-procedure. Integration for A and p>2 is done by a MC-procedure. |
| Usage: | {A,b,V,ctrl}=ICerz(e,FI,A0,b0,N,eps,itmax,expl,fact0,aus) | |
| Input: | ||
| e | numeric; efficiency loss to attain | |
| FI | p x p; Fisher-Information | |
| A0 | p x p; starting value for A; if 0 is entered I^{-1} is taken else if p>1 and dim(A0)==1 FI^{-1}*A0 is taken and if p==1 and A0<0 , -A0/FI is taken | |
| b0 | numeric; starting value for clipping height; if 0 is entered 4*max(vec(abs("A0"))) [i.e. perhaps modified] | |
| N | integer; MC-sample size / integration grid-points | |
| eps | numeric; exactitude | |
| itmax | integer; maximal number of ICerztions | |
| expl | numeric; threshold for the changes in abs. value of A: beyond this value convergence is uncertain ~ 4 | |
| fact0 | numeric (>1)!; factor determining how fast we descend from b to b | |
| aus | integer; 0: no output during execution, 1: some output, 2: more output, 3: a lot of output | |
| Output: | ||
| A | p x p; Lagrange-Multiplyer solving (1) | |
| b | 1; clipping height | |
| V | p x p; corresponding Covariance | |
| ctrl | integer; tells if convergence "happened" | |
Is called by calibrIC.
Calles [within kalman.lib] itera, abinfonewton.
The Output produced if aus>=1 is not identical with the output parameters. (aus>=1) is for interactive use , success is controlled by "verbal" output. (aus==0) is for other quantlets calling ICerz; success is controlled by variable "ctrl".
to be looked up in rICfil
n/a