gmci.default {ctmcd}

Confidence / Credibility Intervals for Generator Matrix Objects

Description

Default function to derive confidence / credibility intervals for "EM" or "GS" based generator matrix objects

Usage

## Default S3 method:
gmci(gm, alpha, eps = 1e-04, cimethod="Direct", expmethod = "PadeRBS", ...)

Arguments

gm

a "EM" or "GS" generator matrix object

alpha

significance level

eps

threshold for which generator matrix parameters are assumed to be fixed at zero (if "EM" object)

cimethod

"Direct" or "SdR" use analytical expressions of the Fisher information matrix, "BS" emloy the numerical expressions of Bladt and Soerensen, 2009 (if "EM" object)

expmethod

method to compute matrix exponentials (see ?expm from expm package for more information)

...

additional arguments

Details

If gm is based on the "EM" method (expectation-maximization algorithm), the function computes a Wald confidence interval based on the method of Oakes, 1999. IF gm is based on the "GS" method (Gibbs sampler), the function computes an equal-tailed credibility interval.

Value

generator matrix confidence bounds

Author(s)

Marius Pfeuffer

References

G. dos Reis, M. Pfeuffer, G. Smith: Capturing Rating Momentum in the Estimation of Probabilities of Default, With Application to Credit Rating Migrations (In Preparation), 2018

Examples

data(tm_abs)

## Maximum Likelihood Generator Matrix Estimate
gm0=matrix(1,8,8)
diag(gm0)=0
diag(gm0)=-rowSums(gm0)
gm0[8,]=0

gmem=gm(tm_abs,te=1,method="EM",gmguess=gm0)

## Oakes Confidence Interval
ciem=gmci(gmem,alpha=0.05)
ciem