## File: gmci.Rd

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r-cran-ctmcd 1.4.1-2
 1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768 \name{gmci} \alias{gmci} \title{ Confidence / Credibility Intervals for Generator Matrix Objects } \description{ Generic function to derive confidence / credibility intervals for "EM" or "GS" based generator matrix objects } \usage{ gmci(gm, alpha, ...) } \arguments{ \item{gm}{ a "EM" or "GS" generator matrix object } \item{alpha}{ significance level } \item{...}{additional arguments: \itemize{ \item{eps:}{ threshold for which generator matrix parameters are assumed to be fixed at zero (if "EM" object) } \item{cimethod:}{ "Direct" and "SdR" use analytical expressions of the Fisher information matrix, "BS" employs the numerical approach of Bladt and Soerensen, 2009 (if "EM" object) } \item{expmethod:}{ method to compute matrix exponentials (see \code{?expm} from \code{expm} package for more information) } } } } \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. } \references{ M. Bladt and M. Soerensen. Efficient Estimation of Transition Rates Between Credit Ratings from Observations at Discrete Time Points. Quantitative Finance, 9(2):147-160, 2009 D. Oakes. Direct calculation of the information matrix via the EM algorithm. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(2):479-482, 1999 G. Smith and G. dos Reis. Robust and Consistent Estimation of Generators in Credit Risk. Quantitative Finance 18(6):983-1001, 2018 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 } \author{ Marius Pfeuffer } \examples{ \dontrun{ 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 } }