You may want to look at the following paper. Best, Giovanni
Reference Type: Journal Article Author: Pinheiro, José C. Author: Bates, Douglas M. Primary Title: Unconstrained parametrizations for variance-covariance matrices Journal Name: Statistics and Computing Cover Date: 1996-09-01 Publisher: Springer Netherlands Issn: 0960-3174 Subject: Computer Science Start Page: 289 End Page: 296 Volume: 6 Issue: 3 Url: http://dx.doi.org/10.1007/BF00140873 Doi: 10.1007/BF00140873 On Fri, 2011-11-18 at 06:07 -0800, Pacin Al wrote: > Hi, > > I would like to know what should I garantee about P and GGt in order to have > > F = Z %*% P %*% t(Z) + GGt always as a positive definite matrix. > > Being more precise: > > I am trying to find minimum likelihood parameters by using the function > 'optim' to find the lowest value generated by $LogLik from the function > 'fkf' (http://127.0.0.1:27262/library/FKF/html/fkf.html). > > The variable Kt within the algorithm used to generate the Kalman Filter > equations needs in each iteration the inverse of the variable Ft, ("Kt[,, i] > = Pt[,, i] %*% t(Zt[,, i]) %*% solve(Ft[,, i])") which is updated by "Ft[,, > i] = Zt[,, i] %*% Pt[,, i] %*% t(Zt[,, i]) + GGt[,, i]". > > Zt is a constant 2x4 matrix and can't be changed. Gt (2x2) and P0 (4x4) are > inputs for 'fkf'. Pt is updated in each iteration, starting with P0. GGt is > constant and one of the parameters tested by 'optim' to minimize the LogLik > (by the way, GGt is always positive definite). Except for the first > parameters that I give to 'optim', I can't control its tested parameters, > which will be used as the inputs of 'fkf' (except, as I sad, for Gt, because > I ask 'optim' to give GLt, the lower triangular matrix of Gt, giving as > input to 'fkf' GLt %*% t(GLt) ). > > Since the process stops every time a non positive matrix Ft appears, I would > like to know if are there any transformations that could be applied to GGt > and P0, given by 'optim', to be sure that Ft will be always positive > definite. > > > > > > > -- > View this message in context: > http://r.789695.n4.nabble.com/Ensuring-a-matrix-to-be-positive-definite-case-involving-three-matrices-tp4083376p4083376.html > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Giovanni Petris <gpet...@uark.edu> Associate Professor Department of Mathematical Sciences University of Arkansas - Fayetteville, AR 72701 Ph: (479) 575-6324, 575-8630 (fax) http://definetti.uark.edu/~gpetris/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
